28 CT07 Abstracts

CP1

Nonlinear Controller Design Based on PiecewiseLinear Approximations

In this paper a general approach to the design of controllersfor Nonlinear Control systems is presented. The method-ology uses a Piecewise Linear (PWL) approximation of theOrdinary Differential Equations (ODEs) vector field whichdescribes the dynamics of a system parameterized by thecontrol inputs in order to exploit the linear properties ofthe PWL vector field facilitating the design of an stabi-lizing controller. The controller design can be carried outinto the PWL approximation and with mild assumptionsis possible to ensure the same asymptotic properties forreal and approximate vector fields. A measure of the dy-namics approximation error is used to estimate upper andlower bounds for the error between the actual and the ap-proximated trajectories once the control vector calculatedwith the PWL system is replaced into the real one. Acase study is presented in order to contrast the theoreticalresults along the paper.

Andres G. GarciaDepto. Ingenera Electrica y de ComputadorasUniversidad Nacional del Sur, Argentinaagarcia@uns.edu.ar

Silvina Biagiola, Jose Figueroa, Liliana Castro,Osvaldo AgamennoniUniversidad Nacional del Surbiagiola@criba.edu.ar, figueroa@uns.edu.ar,lcastro@uns.edu.ar, oagamen@uns.edu.ar

CP1

Impulsive Synchronization of Lipschitz ChaoticSystems

Impulsive method is suitable for digital implementation ofsecure communication based on chaos synchronization. Inthe present study, we assume that the system satisfies thelocally Lipschitz condition and the Lipschitz constant isestimated a priori. We propose an impulsive controller toachieve synchronization of chaotic systems. Moreover, wediscuss the relation between the impulsive intervals and thecontrolling gain. The Chua circuit system is simulated toillustrate the theoretical analysis.

Chien-Cheng Chang, Yen-Sheng ChenDivision of Mechanics, Research Center for AppliedSciences,Academia Sinica,mechang@gate.sinica.edu.tw, ysc@gate.sinica.edu.tw

CP1

The Existence of a Solution to a Free-BoundaryProblem Arising in Blood Flow Modeling

We prove the existence of a solution to a free boundaryproblem modeling blood flow in viscoelastic arteries. Themodel equations are obtained using asymptotic reductionfrom the incompressible, viscous Navier-Stokes equations,coupled with the linearly viscoelastic membrane equations.The reduced, effective equations are defined on the cylin-drical geometry. The resulting problem is nonlinear with afree boundary. The existence of a weak solution is obtainedby using the fixed point arguments.

Suncica Canic, Taebeom KimDepartment of Mathematics

University of Houstoncanic@math.uh.edu, taebeom@math.uh.edu

Giovanna GuidoboniUniversity of HoustonDepartment of Mathematicsgio@math.uh.edu

CP1

Constrained Maneuvering of Autonomous Space-craft Using Potential Function Guidance

Autonomous spacecraft guidance laws constructed fromfunctions that satisfy Lyapunov’s second theorem of stabil-ity or Laplace’s equation are presented. Constrained mo-tion is specified by using the linear superposition of func-tions that describe goal points and regions to avoid. Themethods are appealing since the motion can be visualisedas either that of a particle on an energy surface or in anideal fluid and are suitable for safety–critical applications.Numerical simulations illustrate the methods.

Ender St. John-OlcaytoThe MathWorks, Inc.eolcayto@theiet.org

CP1

Delayed State Feedback Induced Periodic Motions

This paper consider a state self-feedback system wherethe time delay comes from the transfer signal of the feed-back.To investigate delay-induced periodic motion derivedfrom a Hopf bifurcation both quantitatively and quali-tatively, a called perturbation-incremental scheme (PIS),is proposed. Two example are used to demonstrate thepresent method. The validity of the results is shown bytheir consistency with the numerical simulation. Further-more, an approximate solution can be calculated to anyrequired accuracy.

Jian XuSchool of Aerospace Engineering and Applied MechanicsTongji Universityxujian@mail.tongji.edu.cn

Kwow-Wai ChungDeaprtment of MathematicsCity University of Hong Kongmakchung@cityu.edu.hk

CP2

Hereditary Portfolio Optimization in Infinite Di-mensions

This paper treats an infinite time horizon hereditary port-folio optimization problem in a market that consists of onesavings account and one stock account. The savings ac-count compounds continuously with a fixed interest rateand the stock account keeps track of the inventories ofone underlying stock whose unit price follows a nonlin-ear stochastic hereditary differential equation. Within thesolvency region the investor is allowed to consume fromthe savings account and can make transactions betweenthe two assets subject to paying capital-gain taxes as wellas a fixed plus proportional transaction cost. The in-vestor is to seek an optimal consumption-trading strat-egy in order to maximize the expected utility from thetotal discounted consumption. The portfolio optimization

CT07 Abstracts 29

problem is formulated as an infinite dimensional stochas-tic classical-impulse control problem due to the hereditarynature of the stock price dynamics and inventories. Thequasi-variational HJB inequality (QVHJBI) for the valuefunction is derived and the verification theorem for the op-timal strategy is obtained. It is also shown that the valuefunction is a viscosity solution of the QVHJBI.

Mou-Hsiung ChangU. S. Army Research OfficeMathematics Divisionmouhsiung.chang@us.army.mil

CP2

Differential Game Between Manufacturer, Re-tailer, and Bank

We consider a differential game between manufacturer, re-tailer, and bank. The model is a nonlinear system of threedifferential equations with five controls. The first equationdescribes the rate of change of the total assets of the man-ufacturer consisting of loan, value of the inventory, andaccounts receivable. The second equation describes therate of change of the manufacturer’s inventory. The lastequation describes a retailer’s inventory.{

x(t) = K(t) + p2u1(t)π(x(t)) − γx(t),y(t) = −v(t)y(t) + u2(t)π(x(t)),z(t) = −w(t)z(t) + v(t)y(t), t ∈ [0, T ],

(1)

Problems of profit maximization are stated and solved. Op-timal strategy for each player is obtained using MaximumPrinciple and is also recognized as Stackelberg equilibrium.

Evgenii KhailovMoscow State Universitykhailov@cs.msu.su

Ellina V. GrigorievaTexas Woman’s UniversityDepartment of mathematics and computer sciencesegrigorieva@twu.edu

CP2

Scheduling Multiskill Call Centers Using DynamicRouting

In this talk, we address the shift-scheduling problem ina multi-skill call centre. We propos a decision approachplan-operation into two models: plan and operation. Theplanning step we use the queuing theory models to planthe number of agents of each type needed on each period.Then, the operation step tries to produce the planned ex-pectations, this is done by developing a dynamic routingrules. Finally, we develop a simulation model to evaluatethe service level for each call type. Computation resultsobtained from real-life instances are reported

Mohamed Hamdounicomputer and operations research departementmontreal universityhamdounm@iro.umontreal.ca

CP2

Lowering Expected Transaction Costs Via Options

A portfolio with stock and cash cannot be improved by theaddition of an option under the Black Scholes model. Weshow, however, that options are useful if we add transaction

costs to the model. Specifically, for small transaction costsof size ε, the optimal rate for transaction costs without

options is O(ε

23

). With options, however, we explicitly

show the optimal stock/cash/options ratio, which reduces

the optimal cost rate to O(ε

67

).

Dan OstrovSanta Clara Universitydostrov@scu.edu

Jonathan GoodmanCourant Institute of Mathematical Sciences,New York Universitygoodman@courant.nyu.edu

CP3

Bases for the Shuffle Algebra

Combinatorics and free Lie algebras have been used to de-scribe nonlinear control systems. Of interest are the canon-ical projection maps defined using the convolution productin End(A(Z)), where A(Z) denotes the free associative al-gebra over the alphabet Z. Also of interest are the adjointprojection maps. The kernel of these adjoint maps havemany properties that provide, in part, a change of basisfrom that associated with the coordinates of the first kindand the shuffle algebra.

Eric GehrigDept. of Math. and StatisticsArizona State Universityeric@mathpost.la.asu.edu

Matthias KawskiDepartment of Mathematics and StatisticsArizona State Universitykawski@math.la.asu.edu

CP3

Convex Matrix Inequalities in Matrix Unknowns

The talk concerns the question of which Matrix Inequali-ties MIs convert to Linear Matrix Inequalities LMIs or toConvex Matrix Inequalities CMIs. The are two situationswhich behave differently: one whose structure does not de-pend on the dimension of the problem (called dimensionfree) and one which does. A well supported conjecture is:for dimension free problems every CMI results from an as-sociated LMI. The talk will discuss this and whether or notone can determine which MIs transform to CMIs.

J. William HeltonMath. DeptUC San Diegohelton@math.ucsd.edu

CP3

Cross Gramians for Approximate Balancing ofNonlinear Systems

We extend the cross-Gramian method for approximatinglinear symmetric systems, see [D. C. Sorensen, A. C. An-toulas, ”The Sylvester equation and approximate balancedtruncation”, Linear Algebra and Its Applications, vol.351-352, p. 671-700, 2002.], to nonlinear symmetric sys-tems. We study the concept of duality and symmetry for

30 CT07 Abstracts

nonlinear systems, see [J. M. A. Scherpen, ”Duality andsingular value functions of the nonlinear normalized rightand left coprime factorizations.”, Proceedings of the 44thIEEE CDC-ECC, p. 2254-2259, 2005.]. A square non-linear system is called symmetric if it is equivalent to itsdual via a change of coordinates. The duality and sym-metry of nonlinear systems are studied here in the con-text of a non-trivial extension of the linear case. For sym-metric systems we define a cross-operator and cross-energy(Gramian) function related to a nonlinear Sylvester equa-tion. We study the relation between the singular valuefunctions of the cross-energy/operator and the Hankel sin-gular values of the system, starting from [K. Fujimoto,J. M. A. Scherpen, ”Nonlinear Input-Normal RealizationsBased on the Differential Eigenstructure of Hankel Opera-tors”, IEEE Trans. On Aut. Control, vol. 50, 2005.].

Tudor C. Ionescu, Jacquelien ScherpenRijksuniversiteit Groningent.c.ionescu@rug.nl, j.m.a.scherpen@rug.nl

CP3

H-Infnity for Uncertain Systems

Abstract not available at time of publication.

Jung Eun SonUniversity of FloridaDept. of Electrical and Computer Engineeringson@list.ufl.edu

CP4

Viscosity Solutions for Max-Concave Hamiltoniansand Singular Characteristics

Hamilton-Jacobi equationsof the form −mini Hi(x,∇u(x)) = 0 arise in differentialgames where the minimizing player has only a finite num-ber of options. We consider “co-dimension 1” singulari-ties for viscosity solutions, in which discontinuities in thederivative occur across a smooth surface. These can beclassified in a simple way, and described using Melikyan’ssingular characteristics. An example will illustrate how sin-gular characteristics can be used to construct the desiredsolution.

Martin V. DayVirginia Techday@math.vt.edu

CP4

Natural Observers for Second-Order BilinearInfinite-Dimensional Systems

We consider the observer design for a class of second or-der bilinear infinite dimensional systems. In order to pre-serve the physical interpretation of the second order sys-tem, namely that the derivative of the estimated positionis the estimated velocity, we consider the observer in thesecond order setting. We extend earlier results on the nat-ural observers for second order linear infinite dimensionalsystems. Within the arguments for well-posedness for theproposed natural observer, we provide the class of secondorder systems for which the proposed observer design isapplicable, and through a parameter-dependent Lyapunovfunction for second order systems, the stability and con-vergence of the resulting state estimation error (positionand velocity) are established. Extensive simulation stud-ies of a 1D elastic structure describing cable dynamics are

included to further support the theoretical findings of theproposed observer design.

Michael DemetriouWorcester Polytechnic Institutemdemetri@wpi.edu

Fariba FahrooAir Force Office of Scientific Researchfariba.fahroo@afosr.af.mil

CP4

Zero Dynamics Boundary Control for ViscousBurgers’ Equation

In this talk we present our recent results on zero dynamicsdesign applied to a viscous Burgers’ equation. The mainproblem of interest is tracking of time dependent referencesignals prescribed at the ends of a unit interval. The de-sired controls are obtained by application of a zero dynam-ics methodology which has proven to be quite useful forcertain types of (co-located) boundary control problems.We also provide several interesting examples. The mainobstacles encountered in obtaining our main results stemfrom the lack of global a priori estimates for the boundarycontrolled Burgers’ equation.

Victor ShubovUniversity of Massachusetts LowellVictor Shubov@uml.edu

David S. GilliamTexas Tech UniversityDepartment of Mathematics and Statisticsdavid.gilliam@ttu.edu

Chris ByrnesWashington University, St. LouisElectrical and Systems Engineeringchrisbyrnes@wustl.edu

Changbing HuMissouri State UniversityDepartment of Mathematicschangbinghu@missouristate.edu

CP4

Control of Scalar Conservation Laws with Point-wise Sources

An explicit gradient-based algorithm is presented to steerthe distributed state of a scalar conservation law, the con-trol variable being a set of pointwise sources. First, thewellposedness of such equations and their linearized coun-terparts are adressed. A specific adjoint calculus frame-work is then developed for BV fields, nonlinear conserva-tion laws being known to generate such irregular flows. Theefficiency of an adjoint-based gradient scheme is shown onan application in freeway traffic management.

Denis V. JacquetInstitut National Polytechnique de Grenobledenis.jacquet@lag.ensieg.inpg.fr

CP4

The Heat and Schrodinger Equations: Null Bound-

CT07 Abstracts 31

ary Control in One Shot

We discuss the null boundary controllability of the heatand Schrodinger equations with a potential. This unifiedapproach applies not just to both of these PDEs, but alsoto a one-parameter family of PDEs that they belong to.

Stephen W. TaylorUniversity of AucklandMathematics Departments.taylor@auckland.ac.nz

Walter LittmanUniversity of MinnesotaDepartment of Mathematicslittman@math.umn.edu

CP4

Determining Mechanism from Quantum ControlData

Optimal control by closed-loop procedures produces laserpulses which control the dynamic behavior of quantum sys-tems in simulations and experiments. The mechanism ofinteraction between laser and system is not well under-stood. Mechanism may be quantified through an expan-sion of the time propagation operator, and we have pro-posed Hamiltonian encoding to calculate it. We presentthe method, and recent analysis of fundamental limits to,and the feasibility of, an extension suitable for laboratoryuse.

Richard SharpUniversity of Texas at Austinrsharp@ices.utexas.edu

CP5

Circuit Modeling Approach to Analyze the Effectof High Heat on Thermoregulatory Control Mech-anism in Human

Physiological control mechanism cannot be understood un-til its receptor, center of coordination and effector organshave been identified, and until the quantitative relationsbetween the physical stimuli and physiological responses,have been confirmed. The present model circuit has beensimulated using the software MULTISIM that mimics thevasomotor control of human under heat stress. The in-put has been taken as voltage source V2. The minimumskin blood flow (SkBF) has been observed at 35C i.e.,0 ml.100ml-1.min-1 and the maximum at 42C i.e., 18.6ml.100ml-1.min-1. SkBF found to be in accordance withthe physiological process. Hence, modeling using circuittechnique could serve reasonable output.

Rakesh Kumar Sinha, Bhuwan Mohan Karan, BardaNand DasBirla Institute of TechnologyMesra, Ranchi-835215rksinha res@rediffmail.com, bmkaran@bitmesra.ac.in,bndas71@hotmail.com

Yogender AggarwalBirla Institute of Technology, Mesrayogender.aggarwal@gmail.com

CP5

Reduced Models for Neural Control of Respiration

in Mammals

We have developed reduced mathematical models for con-trol of respiration in mammals. The neural controller isdescribed mathematically by a set of differential equationsthat represent respiratory rhythm generation in the brain-stem and was coupled to simplified models of the lungsincorporating oxygen and carbon dioxide transport. Bothfrequency and amplitude of breathing are regulated in re-sponse to physiological control signals (oxygen and carbondioxide). Some features of experimental data are capturedby the model.

Jeffrey C. SmithNINDSNIHjsmith@helix.nih.gov

Alona Ben-TalMassey UniversityInstitute of Information & Mathematical Sciencesa.ben-tal@massey.ac.nz

CP5

Optimal Treatment Planning in RadiotherapyBased on Boltzmann Transport Equations

A Boltzmann transport model for dose calculation in exter-nal radiotherapy is considered. We formulate an optimalcontrol problem for the desired dose. Based on this modelwe develop a direct optimization approach based on ad-joint equations. We prove existence and uniqueness of theminimizer. Numerical results in one and two dimensionsare presented.

Martin Frank, Matthias SchaeferTU KaiserslauternDepartment of Mathematicsfrank@mathematik.uni-kl.de,mschaefer@mathematik.uni-kl.de

Michael HertyTechnische Universitaet KaiserslauternFachbereich Mathematikherty@mathematik.uni-kl.de

CP5

Parameter Identification for Reaction-DiffusionEquations Modeling Turing Patterns

This talk focuses on a reaction-diffusion system modelingpattern formation in developmental biology (morphogene-sis). Optimal control theory is used to find the parame-ters that lead to patterns mimicking those found in na-ture, which is an improvement on the common ad hocapproaches applied previously. The basic approach is tominimize a cost functional that measures the discrepan-cies between a given state called the ’target’, in this case apattern found in nature, and the solution of the reaction-diffusion system. The parameters of the system are treatedas distributed controls. The results of some numerical ex-periments in 2-D are presented using the finite elementmethod, which illustrates the convergence of a variable-step gradient algorithm for finding the optimal controls ofthe system.

Catalin TrencheaUniversity of Pittsburghtrenchea@pitt.edu

32 CT07 Abstracts

Marcus R. GarvieUniversity of Guelph, Ontario, Canadamgarvie@uoguelph.ca

CP5

Dynamics and Impact of the Immune Response toChronic Myelogenous Leukemia

Patients taking Gleevec have a brief but significant immuneresponse against chronic myelogenous leukemia (CML).Our experiments show that these immune cells can be ex-panded in vitro via stimulation with autologous cryopre-served leukemia cells. We formulate a delay differentialequation model of immune and leukemia dynamics, anddevise optimal strategies of vaccination with cryopreservedleukemia cells. We show that vaccinations in combinationwith Gleevec treatment, may significantly increase patientsimmune responses and eliminate CML.

Christiane ChenDivision of HematologyStanford School of Medicineciuchen@stanford.edu

Holden MaeckerBecton Dickinsonholden maecker@bd.com

Doron Levy, Peter S. KimStanford Universitydlevy@math.stanford.edu, pkim@math.stanford.edu

Peter LeeStanford UniversitySchool of Medicineppl@stanford.edu

CP5

Optimal Management of Drug Resistance in Sup-pressive Therapy

Drug resistance in HIV is overwhelmingly likely to pre-exist the start of treatment, and the risk of resistance isproportional to the population of the virus at the start ofdrug treatment. We use models which track populations ofwild-type and drug-resistant virus to show that the currentmethod of replacing a failing drug regimen is non-optimal,and may increase the risk of resistance emerging to thenew regimen. Treatment interruptions using the failingdrug regimen can be used to decrease this risk.

Ryan M. ZurakowskiUniversity of Delawareryanz@ece.udel.edu

CP6

Study of the Dynamic Performance of Pem FuelCells

This paper presents a dynamic nonlinear model for Poly-mer Electrolyte Membrane (PEM) Fuel Cells. A nonlinearcontroller is designed based on the proposed model to pro-long the stack life of PEM fuel cells. Since it has beenknown that large deviation between hydrogen and oxygenpartial pressures can cause severe membrane damages inthe fuel cell, feedback linearization is applied to the PEMfuel cell system such that the deviation can be kept assmall as possible during disturbances or load variations.

Dynamic PEM Fuel Cell model is proposed as a nonlin-ear multiple-input multiple-output (MIMO) system so thatfeedback linearization can be directly utilized. During thecontrol design, hydrogen and oxygen inlet flow rates aredefined as the control variables, and pressures of hydrogenand oxygen are appropriately defined as the control objec-tives. The proposed dynamic model was tested by compar-ing the simulation results and the experimental data previ-ously published. Simulation results show that the proposeddynamic nonlinear PEMFC model has better transient per-formances comparing with the linear control of PEMFC.

Bei GouEnergy System Research CenterUniversity of Texas at Arlingtonbgou@uta.edu

Woonki NaUniversity og Texas at Arlingtonwkna@uta.edu

CP6

An Adaptive Control of Automated Guided Vehiclein Consideration of Mass Change

In this presentation, an adaptive control design of Auto-mated Guided Vehicle (AGV) is proposed. This AGV canmove to all directions by using two active dual-wheel casterassemblies. For the driving construction, the number ofinput is larger than the number of output. The proposedmethod can make an adaptive controller to the redundantsystem. We show that this controller is valid for a changeof loading weight by simulation.

Koichi HidakaElectrical Engineeringhidaka@e.dendai.ac.jp

CP6

Fractional Derivative Model of Edfa with Ase

The present work introduces fractional derivative typemodel into the light amplification in Erbium-doped fiberamplifiers area describing amplified spontaneous emissionof ions. Fractional derivative type model provides a natu-ral framework for generalization of a Bononi type nonlinearmodel in the controllable form. Simulation results of non-linear fractional differential equations based on expansionformula obtained by Atanackovic and Stankovic are alsopresented.

Zoran D. JelicicUniversity of Novi Sad, Faculty of Engineeringjelicic@uns.ns.ac.yu

Nebojsa PetrovackiElectronics/Controls EngineerMcCROMETER, Hemet, CA 92545-7799 USAmailto:nebp@mccrometer.com

CP6

Comparison of Control Methodologies for a BenchMark Line of Sight Stabilization Application

This work presents control law designs for a benchmark,line-of-sight stabilization application for Electro-opticalsystems mounted on mobile platform, using representativemethodologies like Open loop shaping, H-infinity control

CT07 Abstracts 33

method and Fuzzy Knowledge based controller. All thecontrollers meet the stringent requirements of disturbanceattenuation and command following. Different method-ologies are compared for their relative merits and demer-its with respect to ease of design, implementation andperformance in presence of practically unavoidable non-linearities.

Rajeev Marathe, J A R Krishna Moorty, Hari BabuSrivastavaInstruments Research & Development EstablishmentDehra Dun, Indiarajeev marathe@rediffmail.com, krish@irde.res.in,hari b sriv@rediffmail.com

CP6

A Study on Thermal Control in Small-Scale Elec-tricity Furnace by Thermal Regulator E5EN-R1T

In this paper, thermal control result of the small-scaleelectric furnace model by the thermal regulator E5EN-R1T is described. Based on results of ON-OFF controlin this model, proportional band can be adjusted the firstthing. Then, the authors set the values of P(proportion),Ti(Integration)and Td(Differential) by trial-error methodon the theory(Marginal sensitivity theorem),and P control,PI control and PID control are carried out. A pretty goodcontrol result(P:60C,Ti:60sec, Td:30sec) has been obtainedand it is reported.

Hayato OkadaSeminar student in HiroshimaKokusai Gakuin Universityt.munakata@hkg.ac.jp

Kahar SamsakResearcher in HiroshimaUniversityt.munakata@hkg.ac.jp

Tsunehiro MunakataProfessor, Mechanical Engineering inHiroshima Kokusai Gakuin University, JAPANt.munakata@hkg.ac.jp

CP7

On the Stability of Some Stochastic Integral Equa-tions

Stochastic Volterra equations of the form:

dx(t) = f(x(t))dt +

∫ t

0

K(t− s)x(s)ds dt + g(x(t))dB(t),

are considered, where {B(t) : t ≥ 0} is standard one - di-mensional Brownian motion and the kernel K decreases tozero non-exponentially. We study the convergence rate tozero of the stochastic solutions of the considered equation.It is proved under suitable conditions that :

limt→∞

|x(t)|K(t)

= ∞, almost surely.

The considered stochastic integral equations arise if we con-sider the Black-Scholes market consists of a Bank accountor a bond and a stock. These stochastic models can alsobe applied to population dynamics in biology.

Khairia El-Said A. Abd El-Fattah El-NadiProfessor of mathematical statistics

Faculty of science Alexandria University Egyptkhairia el said@hotmail.com

CP7

A Forward-Backward Algorithm for PerturbedStochastic Linear-Quadratic Regulator Problems

We consider a nonlinear perturbation in the drift coeffi-cient of the state equation for a linear-quadratic regulator(LQR) problem. We propose a forward-backward numeri-cal algorithm to solve this optimization problem using therepresentation theorems between forward-backward SDEsand stochastic control problems. We identify certain regu-larity and growth conditions for a smooth solution to thecorresponding HJB equation as well as to the FBSDE sys-tem. We also discuss convergence and regularity propertiesof the proposed scheme.

Coskun CetinCalifornia State University, Sacramentocetin@csus.edu

CP7

On a Stochastic Robust Control

We consider some stochastic dynamical systems,which rep-resents robustness that arise in controller and filter designsand also represent a remote control system in the presenceof a network cable. The flexible arms connected by elasticjoints of the robot is also studied. In addition we introducea theory about the artificial intelligence. Some determinis-tic fractional dynamical systems is studied. These systemshave many applications in robot and industry.

Mahmoud Mohamed M. Mostafa El-BoraiProfessor of mathematicsFaculty of science Alexandria University Egyptm m elborai@yahoo.com

CP8

Linear Quadratic Analysis of Tcp/ip NetworksTransients

In this paper we consider a transient regime analysis forlinearized models of TCP/IP networks in terms of theircongestion signaling and queueing dynamics. Assumingthe network information is known when compensating fordelays, a linear quadratic control framework is invoked tocalculate the robust control gains. The delay independentcontrol has performance limits for large network delays,whereas the delay dependent control used in this paperregulates the delay closed loop dynamics arbitrarily close.

Alexandru MurguBT Networks Research Centrealexandru.murgu@bt.com

CP8

Hierarchical Fault Tolerant Control of NetworkService Availability

This paper is concerned with the mathematical analysis ofa hierarchical Fault Tolerant Control (FTC) framework forservice availability in communication systems. Followinga control and optimization perspective, a modular designprocedure for diagnostic and reconfiguration algorithmsrunning at different levels of the hierarchy is described. Ahierarchical decision logic algorithm is obtained by invok-

34 CT07 Abstracts

ing the theoretical devices of the supervisory control theoryof discrete event systems. Numerical results supporting thetheoretical findings are provided.

Alexandru MurguBT Networks Research Centrealexandru.murgu@bt.com

CP8

Stabilizing Controllers over Networks

This talk considers the problem of finding decentralizedcontrollers which stabilize a network of subsystems whenthe controllers may communicate, but subject to delays.When all of the subsystems and associated controllers un-der consideration are linear time-invariant, a conditioncalled quadratic invariance allows for the parameterizationof all stabilizing controllers, and it is shown that for thisproblem, that condition reduces to controllers being able tocommunicate information faster than dynamics propagate.A new invariance condition has been shown to similarly al-low for the parameterization of all possibly nonlinear, pos-sibly time-varying stabilizing controllers. It is shown thatthis also reduces to the controllers being able to share in-formation faster than dynamics propagate, so that if theydo, one may find all causal stablizing controllers over thenetwork.

Michael C. RotkowitzThe Australian National UniversityResearch School of Information Sciences and Engineeringmichael.rotkowitz@anu.edu.au

CP9

Control of a Three-Joint Underactuated PlanarManipulator by Interconnection and Damping As-signment Passivity-Based Control Method

We apply Interconnection and Damping AssignmentPassivity-Based Control (IDA-PBC) method to an un-deractuated planar manipulator with the third joint un-actuated which is under second-order nonholonomic con-straints. We give a port-Hamiltonian representation of thesystem and present the applicable condition of IDA-PBC.We also design a desired inertia matrix and potential en-ergy function of the closed Hamiltonian system to derivea concrete control law. Numerical experiments show theeffectiveness of the controller.

Naohiro TodaFaculty of Information Science and Technology,Aichi Prefectural Universitytoda@ist.aichi-pu.ac.jp

Masahide ItoFaculty of Information Science and TechnologyAichi Prefectural Universitymasa.ito@toda.ist.aichi-pu.ac.jp

CP9

Vibration and Control of a Flexible Structure withVariable Joint Stiffness

In most structure analyses, the joint stiffness is typicallyneglected. For structures operating in a harsh environ-ment; e.g., the landing gears of an aircraft, or structuresof off-shore oil platform, once the joint stiffness is reducedto the level of links, it provides almost no support to the

system, and ensuing failure is expected. In this study, weinvestigate the effects of variable joint stiffness on the vi-bration of a simple beam structure. The natural frequencyof the beam structure is first examined at different levelof joint stiffness, from which a functional relationship canbe established and feasible control algorithms are proposedfor the future design of smart structures.

Chuan LiNanyang Technological Universitymcli@ntu.edu.sg

CP9

Variational Principles and Geometry of Nonholo-nomic and Vakonomic Mechanical Systems

We explore mechanical systems with nonholonomic con-straints that either satisfy i) The Principle of Virtual Work(Dynamics) or ii) Hamilton’s Principle (Vakonomics). Wewill discuss the difference between these two systems in ageometric context, and show how either system can be de-scribed in terms of quasi-velocities. As an illustration ofvakonomic dynamics we consider the fourth order dynam-ical systems that arise from the optimal control of secondorder nonholonomic systems.

Jared M. MaruskinUniversity of Michiganjmaruski@umich.edu

CP9

Task Encoding and Control of MetamorphicRobots

Controlled shape change is an important requirementin many metamorphic systems, including reconfigurablerobots and biological systems. We are interested in theproblem of encoding this task in a dynamical systems set-ting, so as to enable robust behaviors. Towards this end,we present two technical contributions: (a) a techniquefor characterizing the geometry of shape spaces of meta-morphic robots that allows us to design dynamical controlstrategies as vector fields in this space and (b) techniquesfor optimally sampling such spaces, which admit a manifoldstructure, enabling the application of efficient approxima-tion algorithms for computing geodesics.

Lothar WenzelNational Instruments Corp.Austin, TX 78759lothar.wenzel@ni.com

Subramanian RamamoorthyUniversity of Texas at Austins.ramamoorthy@mail.utexas.edu

CP9

Adaptive Backstepping Design of a Two DofFlexible-Joint Robot Based on Function Approx-imation Technique

In this paper a function approximation technique is pro-posed for adaptive backstepping design of a two-linkflexible-joint robot manipulator. The dynamics of therobot manipulator are derived with the assumption thatall matrices in this robot model are unknown. Using theLyapunov stability theory, a set of update law is derived togive closed loop stability with proper tracking performance.

CT07 Abstracts 35

The computer simulation is shown to verify validity and ef-fectiveness of the proposed control law.

Jinsiang ShawMechanical Engineering DepartmentNational Taipei University of Technologyjshaw@ntut.edu.tw

Yin-Chieh ChangInstitute of Mechatronic EngineeringNational Taipei University of Technologykoji90kimo@yahoo.com.tw

CP9

Stability Analysis of a Non-Autonomous ControlSystem Using the Concept of Lyapunov Exponents

A bipedal robot trajectory tracking control system is in-vestigated. Since the biped is subjected to constraints, thevalue of control torque cannot be chosen arbitrarily. A sim-ple harmonic motion is chosen as desired trajectory, whichleads the tracking control system to non-autonomous. Thestability of such non-autonomous system is analyzed us-ing the concept of Lyapunov exponents. Lyapunov expo-nents spectrum is calculated based on mathematical mod-els (of both non-autonomous and autonomous systems) anda time series.

Caixia C. Yang, Qiong WuThe University of ManitobaDepartment of Mechanical and ManufacturingEngineeringwycx425@yahoo.com, cwu@cc.umanitoba.ca

CP10

An Efficient Computational Algorithm for the So-lution of Control Problems with Ill-Posed Model

The solution and analysis of a control problem involves thesolution and analysis of the mathematical model of the re-lated system. Quite often, one can not obtain a closed formsolution/analysis for the model, and thus computationalmethods are to be used. The resulting discrete system isnormally ill-conditioned. In this work, we develop a multi-level computational approach for the solution of these typesof control problems, leading to significant improvements inthe results.

Kourosh ModarresiStanford UniversitySCCMkourosh.modarresi@stanford.edu

Gene GolubStanfordgolub@stanford.edu

CP10

Using The Method of Subdomains in the Solutionof Control Problems

In this work, we divide the domain of the solution into dif-ferent subdomains, based on the common features of thesubdomain. This would allow us to use an adaptive nu-merical algorithm in the solution of the control problems.This algorithm would let us to take into the account thespecific features of each subdomain and treat the problemlocally. We have obtained better results using our method,

as compared to the similar results of the classical globalmethods.

Kourosh ModarresiStanford UniversitySCCMkourosh.modarresi@stanford.edu

Gene GolubStanfordgolub@stanford.edu

CP10

Trust Region Spectral Bundle Method for Noncon-vex Eigenvalue Optimization

We present a nonsmooth optimization technique for non-convex maximum eigenvalue functions and for nonsmoothfunctions which are infinite maxima of eigenvalue func-tions. We prove global convergence of our method in thesense that for an arbitrary starting point, every accumu-lation point of the sequence of iterates is critical. Themethod is tested for the H∞ controller synthesis on someclassical plants. Results are compared with those previ-ously obtained by other techniques.

Pierre ApkarianCert - OneraToulouse, Francepierre.apkarian@cert.fr

Olivier ProtLaboratoire MIPUniversite Paul Sabatieroprot@mip.ups-tlse.fr

Dominikus NollUniversite Paul SabatierMathematiques pour l’Industrie et la Physiquenoll@mip.ups-tlse.fr

CP10

Circuit Design Problem Formulation on Basis ofthe Control Theory Approach

The design process of any analog circuit design was formu-lated on the basis of the control theory application. Thisapproach produces the infinite set of different design strate-gies inside the same optimization procedure. The problemof minimal-time design algorithm construction is definedas the problem of a functional minimization of the controltheory. The design process is defined as a controllable dy-namic system and the Lyapunov function of this systemserves to minimize the computer design time. Numericalresults of some electronic circuit design demonstrate theefficiency of the proposed methodology.

Alexander ZemliakPuebla Autonomous UniversityDept. of Physics and Mathematicsazemliak@fcfm.buap.mx

CP10

Numerical Optimization Assisted by Noncommu-tative Symbolic Algebra

We describe how a symbolic computer algebra tool (NCAl-gebra) that can handle symbolic matrix (noncommutative)

36 CT07 Abstracts

products is used to numerically solve systems and controlproblems. Our current focus is on semidefinite programsarising from control theory, where matrix variables appearnaturally. Our tools keep matrix variables aggregated at allsteps of a primal-dual interior-point algorithm. Symbolicmatrix expressions are automatically generated and usedon numerical iterative procedures for the determination ofsearch directions, showing promising results.

Mauricio de OliveiraMechanical and Aerospace EngineeringUniversity of California at San Diegomauricio@mechanics.ucsd.edu

CP11

Large-Scale Control in Porous Media Flow

Control of porous media flow, such as reservoir manage-ment, is not a new area of research. Since the founda-tions of reservoir simulation and management some kindof optimization has been used in practice. However, flowcontrol in porous media flow has been facing remarkablenew challenges in a theoretical and practical point of view.In this talk, issues in large-scale closed-loop control willbe discussed emphasizing model reduction applied to im-provements in oil recovery.

Hector KlieCenter for Subsurface Modeling, UT Austinklie@ices.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ticam.utexas.edu

Adolfo RodriguezCenter for Subsurface Modeling,UT Austinadolfo@ices.utexas.edu

Eduardo GildinInstitute for Computation Engineering and Sciences -CSMUT Austineglidin@mail.utexas.edu

CP11

Curvature of Optimal Control: Deformation of Pla-nar Systems

The Maximum Principle provides necessary conditions fora trajectory-control-pair to be optimal. Classical sufficientconditions test for definiteness of second order derivatives.Recently Agrachev introduced a curvature of optimal con-trol, which yields elegant sufficient conditions for systemswhose control take values in a circle. We present initialstudies of this curvature as this circle continuously deformsinto a closed interval. Of particular interest is its behaviorat parameter values where conjugate points emerge withassociated loss of optimality.

Parnell Maxwell, Matthias KawskiDept. of Mathematics and StatisticsArizona State Universityparnell.maxwell@asu.edu, kawski@asu.edu

CP11

A Dual Method for the Two-Target DistributedOptimal Control of a Parabolic System

We consider the problem of finding an optimal control thatdrives the solution of the given parabolic PDE to a specifiedtarget at some fixed time. Meanwhile it is desired to keepthe variation of the solution from a second target as smallas possible. We treat this problem as a multi-objectiveoptimization and consider three different approaches forthe solution. We compare these approaches and proposean efficient algorithm based on the duality.

Sung-Sik KwonDepartment of Mathematics and Computer ScienceNorth Carolina Central University, Durham, NorthCarolinaskwon@nccu.edu

Jon TolleDepartment of Statistics and Operations ResearchUniversity of North Carolina at Chapel Hilltolle@email.unc.edu

CP11

Boundary Control Schemes for Nonlinear KirchhoffString

A nonlinear Kirchhoff string is given as

∂2z(x, t)

∂t2= M(‖∂z(x, t)

∂x‖2)

∂2z(x, t)

∂x2, x ∈ (0 , 1) , t ≥ 0 ,

z(0, t) = 0 , M(‖∂z(x, t)∂x

‖2)∂z

∂x(1, t) = u(t) , t ≥ 0 ,

here M(·) ∈ C1(R+), ‖ · ‖ represents L2 norm, u(t) is theboundary control force. We propose two new stabilizingcontrollers by using z(1, t), which are related to the positivereal controllers. One of these classes generalizes a classalready proposed in the literature and the other one is new.

Shahram ShahruzBerkeley Engineering ResearchInstitutebeforedeadline@yahoo.com

Omer MorgulBilkent Univ.Dept. of Electrical Eng.morgul@ee.bilkent.edu.tr

CP11

On the Controllability of Maxwell Fluids

We study the controllability of viscolastic fluids governedby the upper convected Maxwell equation. The effects ofdifferent fluid geometries are investigated. This is a jointwork with Professors Wei Kang and Arthur Krener.

Hong ZhouDepartment of Applied MathematicsNaval Postgraduate School, Monterey, CAhzhou@nps.edu

CP12

A Piecewise Linear Output Error Identification Al-gorithm

We present a novel BIBO stable Nonlinear Output Er-

CT07 Abstracts 37

ror (NOE) identification algorithm based on High LevelCanonical Piecewise Linear (HL CPWL) functions. Start-ing from a linear OE approximation, the model structureallows the implementation of an identification algorithm inwhich the order of the model can be easily increased duringthe identification process retaining the previous achievedapproximation. We also describe the possibilities of thehardware implementation of the identification algorithm.

Osvaldo AgamennoniUniversidad Nacional del Suroagamen@uns.edu.ar

CP12

On the Implementation of a Wavelet-Based Itera-tive Learning Controller Using Cpld/fpga

The implementation of a wavelet-based iterative learningcontroller (WILC) is presented in this paper. To meet therequirements of simple hardware, fast rapid prototypingand cost-effectiveness, we present a servo-chip design witha wavelet-based iterative learning control scheme which isimplemented on a single Altera FLEX 10KRC-240 FPGA(Field Programmable Gate Array). Three sub-systemsare built inside this FPGA-based servo-chip, including afeedback controller module, a discrete wavelet transform(DWT) module and an inverse discrete wavelet transform(IDWT) module. To verify the efficacy of this design, anink-jet printer is adopted as the control target and a muchimproved speed-tracking performance is observed from theexperimental verification. Simulations on Matlab are alsopresented for comparison.

Jian-Shiang ChenDepartment of Power Mechanical EngineeringNational Tsing Hua University, Hsinchu, Taiwanjschen@pme.nthu.edu.tw

CP12

Game-Theoretic Model-Based Approachto Higher-Level Fusion with Application to SensorResource Management

We present a hierarchical game-theoretic approach to level2 and level 3 fusion problems. Given level 1 data of observa-tions of individual objects and prior knowledge of the com-position of enemy grouping, we consider the level 2 problemby developing a Bayesian inference algorithm for determin-ing the enemy identity. We then apply game theory towardthe level 3 problem, inferring the intent of enemy groups,given the determined identities and prior knowledge of en-emy strategies.

Sang ChinSAICPrincipal Scientistshc@alum.mit.edu

CP12

Online Parameter Identification in Time Depen-dent Differential Equations

Online parameter identification becomes necessary when-ever model parameters are needed in order to support deci-sions that have to be taken during the operation of the realsystem. Based on ideas from adaptive control and regular-ization of inverse problems we suggest an online methodthat works both for ODEs and time-dependent PDEs. Itallows for partial state observations and does neither re-

quire a linear parameterization nor data differentiation orfiltering. Numerical examples in context of aircraft controlare presented.

Philipp KueglerJohannes Kepler Universitaet, LinzAustriaphilipp.kuegler@jku.at

CP12

Temperature Data Assimilation Based on Point-wise Transient Measurements: High Speed Vari-ational Reconstruction

The inverse problem of temperature identification basedon pointwise transient measurements is considered. Theproblem is set in a model-based data assimilation approachthat builds upon optimal control theory. The well-knownconvergence difficulty of the adjoint technique near the fi-nal instant is eliminated here by minimizing the regularizedperformance index in a smooth enough functional space. Adual formulation of the problem constructs a high-speed al-gorithm well suited for real-time applications and enablingparallel computations.

Frederic BourquinFrench Public Works Research Laboratoryand GDRE Lagrangefrederic.bourquin@lcpc.fr

Alexandre NassiopoulosFrench Public Works Research Laboratoryalexandre.nassiopoulos@lcpc.fr

CP12

Explaining Learning and Its Various Types by aMulti-Feedback Control Model

In this paper, well clarify relations existing between con-trol, learning and modeling by presenting a computablemodel integrating a set of nested loops of control. Wellfirst explain a 2-loops model, which will be generalized ton loops afterwards. This will allow us to define variouscategories of learning. The specific role of recursivity willbe analyzed. Well illustrate the use of this model on hu-man learning as well as on auto-optimized microelectronicsdigital chips.

Vincent Raman, Frederic RobertUniversite Libre de BruxellesFaculty of Applied Science - BEAMSvraman@ulb.ac.be, frrobert@ulb.ac.be

MS1

On Regularization Concepts for Parabolic Bound-ary Control Problems with Pointwise State Con-straints

The presence of pointwise state constraints presents a chal-lenge for the analysis as well as the numerical treatmentof optimal control problems. It is known that the La-grange multipliers associated with the constraints are reg-ular Borel measures, if the states are considered in spacesof continuous functions. On the one hand, this restric-tion to continuous state functions requires sufficient reg-ularity of the controls. Without box constraints on thecontrol, this leads to severe restrictions on the spatial do-main when considering controls in L2-spaces. In parabolic

38 CT07 Abstracts

boundary control problems, first order necessary optimalityconditions of Karush-Kuhn-Tucker type cannot be shownat all in useful spaces. On the other hand, solving state-constrained optimal control problems numerically leads tospecific difficulties. For example, measures appear in theright-hand-side of associated adjoint equations. In recentyears, many regularization approaches have been studiedin order to improve both the analysis and the numericaltreatment of these problems. In this talk, we apply differ-ent regularization methods to parabolic boundary controlproblems with pointwise state constraints in the whole do-main and compare the results.

Fredi TroeltzschTech Univ of BerlinDepartment of Mathematicstroeltz@math.tu-berlin.de

Ira NeitzelTech University of BerlinDepartment of Mathematicsneitzel@math.tu-berlin.de

MS1

Optimal Control Problems for PDEs with MixedControl-State Constraints – Multiplier Regularityand Numerical Applications

In the optimal control of ordinary differential equa-tions it is a well known fact that problems with mixedcontrol-state constraints exhibit better properties thanthose with pure pointwise state constraints. A sim-ilar behaviour was observed for the optimal controlof elliptic and parabolic partial differential equations,(M. Bergounioux and F. Troltzsch. Optimal control ofsemilinear parabolic equations with state-constraints ofbottleneck type. ESAIM, Control, Optimisation and Cal-culus of Variations, 4:595–608, 1999.), (N. Arada and J. P.Raymond. Optimal control problems with mixed control-state constraints. SIAM J. Control, 39:1391–1407, 2000.),(A. Rosch and F. Troltzsch. Existence of regular Lagrangemultipliers for a nonlinear elliptic optimal control problemwith pointwise control-state constraints. SIAM J. Controland Optimization, xx(x):548–564, 2006.). For instance, theLagrange multipliers associated with certain mixed controlstate constraints are functions of Lp-spaces. Following anapproach suggested in (A. Dmitruk. Maximum principlefor the general optimal control problem with phase and reg-ular mixed constraints. Computational Mathematics andModeling, 4:364–377, 1993.) for ODEs, the talk reports ona new and simplified technique to prove L1-regularity inthe case of elliptic PDEs. Moreover, an idea of (A. Roschand D. Wachsmuth. Regularity of solutions for an opti-mal control problem with mixed control-state constraints.2006, submitted.) is extended to derive L∞-estimates forthe multipliers, along with the proof of Lipschitz regular-ity of optimal controls. The potential application to thenumerical regularization of problems with pure pointwisestate constraints is briefly sketched.

Fredi TroeltzschTech Univ of BerlinDepartment of Mathematicstroeltz@math.tu-berlin.de

Arnd RoeschJohann-Radon Institute (RICAM)Austriaarnd.roesch@oeaw.ac.at

MS1

Error Estimates for Finite Element Discretizationof Parabolic Optimal Control Problems

In this talk we discuss space-time finite element discretiza-tion of parabolic optimal control problems with controlconstraints. We develop a priori error analysis taking intoaccount space and time regularity of the optimal solution.For the treatment of control constraints we generalize andcompare different approaches known from elliptic controlproblems. Numerical results confirm theoretical investiga-tions.

Boris VexlerRICAM, Austrian Academy of Sciencesboris.vexler@oeaw.ac.at

MS1

Adaptive Finite Element Methods for OptimalControl Problems with Control Constraints

We present our work on a posteriori error estimators forthe discretization- error in the cost functional or a givenquantity of interest, for optimal control problems governedby partial differential equations with additional inequalityconstraints on the controls. Afterwards we discuss evalu-ation of local indicators obtained from the estimation foradaptive mesh refinement. Finally we will demonstrate ourresults with some numerical examples.

Winnifried WollnerUniversity of HeidelbergInstitute for Applied Mathwinnifried.wollner@iwr.uni-heidelberg.de

Boris VexlerRICAM, LinzAustriaboris.vexler@oeaw.ac.at

MS2

Correction of Perturbed Optimal Feedback Con-trollers in Real-Time

Open-loop solution of a optimal control problems are justthe first step to cope with the practical realization ofreal life applications. Closed-loop (feedback) controllers,like the classical Linear Quadratic Regulator (LQR), areneeded to compensate perturbations appearing in reality.Although these controllers have proved to be a powerfultool in many applications and to be robust enough to coun-tervail most differences between simulation and practice,they are not optimal if disturbances in the system data oc-cur. If these controllers are applied in a real process, thepossibility of data disturbances force recomputing the feed-back control law in real-time to preserve stability and opti-mality, at least approximately. For this purpose, a numer-ical method based on the parametric sensitivity analysis ofnonlinear optimization problems is suggested to calculatehigher order approximations of the feedback control law inreal-time. Using this method, the optimal controller canbe adapted within a few nanoseconds on an typical per-sonal computer. The method is illustrated by the adaptiveoptimal control of the classical inverted pendulum and acrane system.

Christof BueskensUniversity of BremenBremen, Germany

CT07 Abstracts 39

Bueskens@math.uni-bremen.de

MS2

Steady State and Turnpike of Infinite DimensionalOptimal Control Systems

In this talk we are concerned with the long-run behavior ofsolutions to infinite horizon optimal control problems. Weconsider optimal control systems where the state equationis a semi-linear parabolic equation and the cost integrandis convex. The goal is to establish convergence to steadystate and turnpike property of solutions to infinite horizon,optimal control systems.

Arie LeizarowitzTechnion-Israel Institute of TechnologyHaifa 32000, Israella@techunix.technion.ac.il

MS2

Optimal Control of a Servo Drive System withCoulombic Friction and State Constraints

We consider a servo drive system that represents a typicalelectrodynamic actuator. As such an actuator is very com-mon for loudspeakers, it is called a voice-coil-motor. Thebasic dynamical model comprises five ODEs for the motor,resp., load mass positions and velocities as well as the coilcurrent. The control function is given by the voltage input.The system involves static Coulombic friction that causesdiscontinuities in the dynamic equation for the motor massvelocity. We study both time-minimal and energy-minimalcontrols imposing state constraints for the velocities. Thecomputed optimal controls were implemented on a real sys-tem and turned out to be in perfect agreement with mea-sured test bench results.

Oliver ZirnUniversity of Applied Sciences GiessenFachbereich Elektro- und Informationstechnikoliver.zirn@ei.fh-giessen.de

Helmut MaurerWest Wilhelms- Univ MunsterInst fur Num und Instr Mathmaurer@math.uni-muenster.de

MS2

Suboptimal Feedback Control Design of Con-strained Parabolic Systems in Uncertainty Condi-tions

The talk concerns minimax control problems for linearparabolic systems with uncertain perturbations and con-trol functions acting in the Dirichlet boundary conditions.The parabolic control system is functioning under point-wise constraints on control and state variables. The maingoal is to design a feedback control that ensures the re-quired state performance and robust stability under anyfeasible perturbations and minimize an energy-type func-tional under the worst perturbations from the given area.We develop an efficient approach to the minimax controldesign of parabolic systems that is based on certain prop-erties of the parabolic dynamics. In this way we justifya suboptimal structure of the feedback regulator and com-pute its optimal parameters ensuring robust stability of theclosed-loop, highly nonlinear parabolic control system on

the infinite horizon.

Boris MordukhovichWayne State UniversityDepartment of Mathematicsboris@math.wayne.edu

MS3

Well-Posedness of a Fluid-Structure InteractionProblem Arising in Blood Flow

The speaker will talk about the existence of a unique solu-tion to an initial-boundary value problem arising in mod-eling blood flow through viscoelastic arteries. The prob-lem describes the coupling between the axially symmet-ric flow of an incompressible, viscous fluid modeled by theNavier-Stokes equations and the motion of the vessel wallsmodeled by the linearly viscoelastic membrane equations.Assuming the physiologically relevant flow and vessel walldata with the physiologically relevant inlet and outlet pres-sures, this become a difficult problem to analyze due to thecompetition between the hyperbolic and parabolic effectsdriving the wave propagation in arterial walls smoothed outby the small vessel wall viscosity and the viscous fluid ef-fects. As a first step toward analysing this problem, we de-rived a closed system of effective, reduced two-dimensionalequations that capture the main features of the originalproblem to a certain accuracy. The resulting problem isa two-dimensional, non-linear version of the Biot equa-tions arising in porous media flows. Using energy methodsand fixed-point arguments, we obtained the existence of aunique solution to the resulting non-linear free-boundaryproblem. The numerical solutions were compared with theexperimental flow measurements, performed at the TexasHeart Institute, showing excellent agreement between theexperiment and the solutions of the reduced problem.

Suncica CanicDepartment of MathematicsUniversity of Houstoncanic@math.uh.edu

Giovanna GuidoboniUniversity of HoustonDepartment of Mathematicsgio@math.uh.edu

Taebeom KimDepartment of MathematicsUniversity of Houstontaebeom@math.uh.edu

Andro MikelicUFR Math’{e}matiquesUniversit’{e} Claude Bernard Lyon 1andro@lan.univ-lyon1.fr

MS3

Finite Element Analysis of a Coupled Fluid-Structure System

In this talk, we will consider the numerical analysis ofa fluid-structure interactive partial differential equation(PDE) system, comprising the Stokes (or Navier-Stokes)equations coupled to the equations of linear elasticity.The coupling between the two distinct dynamics is accom-plished on the boundary interface between respective fluid

40 CT07 Abstracts

and structure geometries. Solutions of this fluid-structurePDE are approximated by means of a certain Finite Ele-ment Method (FEM), a FEM which in part incorporatesa nonstandard usage of the Babuska-Brezzi ”inf-sup” The-ory.

George AvalosUniversity of Nebraska-LincolnDepartment of Mathematics and Statisticsgavalos@math.unl.edu

Matt DvorakUniversity of Nebraska-Lincolns-mdvorak1@math.unl.edu

MS3

The Coupled PDE System Arising in Fluid-Structure Interaction

In this talk, a fluid-structure interactive partial differentialequation (PDE) model is considered. The PDE comprisesa coupling of the linearized Stokes equations to a vector-valued wave equation, with this wave equation constitutinga (simplified) model for the structural component of thedynamics. The coupling between the disparate PDEs oc-curs on the boundary interface between the fluid and solidmedia. We shall discuss how an explicit semigroup formu-lation may be given to these linearized dynamics, by virtueof a novel elimination of the associated pressure. We sub-sequently proceed to give a precise characterization of thespectrum of the fluid-structure semigroup generator; be-sides being of acute interest in its own right, this spectralcharacterization allows an appeal to the well-known cri-terion of Arendt-Batty and Lyubich-Phong, so as to inferstrong stability of the fluid-structure semigroup; thus thesolutions to the fluid-structure PDE decay asymptotically.(During the course of this talk, it will be shown that theresolvent of the fluid-structure generator is not a compactoperator; thus strong stability cannot be inferred by theclassical approach of Nagy-Foias).

George AvalosUniversity of Nebraska-LincolnDepartment of Mathematics and Statisticsgavalos@math.unl.edu

Roberto TriggianiUniversity of Virginiart7u@virginia.edu

MS4

Application of Sparse Optimal Control Techniquesin the Aerospace Industry

Combing modern nonlinear programming algorithms thatexploit matrix sparsity with discretization techniques forordinary differential equations has resulted in powerful newcomputational techniques for optimal control. This pre-sentation will deal with some of the important algorithmicissues that must be addressed when applying these newmethods to realistic applications in the aerospace industry.

John T. BettsThe Boeing Companyjohn.t.betts@boeing.com

MS4

Towards Accurate Costates Estimation Using

Pseudospectral Methods

Costates estimation is an important issue in computationaloptimal control. Accurate costates facilitate convergenceanalysis, optimality verification, sensitivity analysis and adesign of robust feedback control systems. In this talk,we analysis the relation between the discrete KKT multi-plies and the continuous costates in the pseudospectral di-rect approximation of continuous constrained optimal con-trol problems. Closure conditions previously discovered areclarified. The effect of primal optimality/feasibility toler-ances to the costate estimation is explained and demon-strated via examples. The results provide guidelines todesign accurate costates estimation algorithms.

Qi GongUniversity of Texas at San AntonioQi.Gong@utsa.edu

Michael RossDepartment of Mechanical and Astronautical EngineeringNaval Postgraduate Schoolimross@nps.edu

MS4

Discrete Approximations in Optimal Control

In this talk we discuss several issues on discrete approxi-mation of optimal control systems governed by controlleddifferential equations and differential inclusions with finite-dimensional and infinite-dimensional state spaces. 1. Thefirst issue is about well-posedness of discrete approxima-tions of constrained optimal control problems. We discussnew results on consistent approximations of endpoint andstate constraints matched with the stepsize of discretiza-tion ensuring the value convergence as well as the strong(in Sobolev spaces) convergence of optimal solutions ofdiscrete approximations. 2. The second issue concernsthe fulfillment of the necessary optimality conditions inthe form of the Approximate Maximum Principle for dis-crete approximations of constrained optimal control prob-lem with no convexity assumptions. There are positiveand negative results in this direction, both are rather sur-prising. 3. Finally, we discuss the possibility to use dis-crete approximations as the driving force to derive newresults (necessary optimality, local controllability condi-tions, etc.) for continuous-time systems by the limitingprocedure from the corresponding problems of mathemat-ical programming.

Boris MordukhovichWayne State UniversityDepartment of Mathematicsboris@math.wayne.edu

MS5

Adaptive Nash Strategies of Dynamic Games inHigh Level Information Fusion

Recent advances in applying game theory to high levelinformation fusion are promising. In those game theo-retic frameworks, adaptive techniques are important whenthere are unknown parameters in the cost functions ofthe opponents. Existing adaptations are usually consid-ered from a perspective of systems, for an example, evo-lutionary games. In this paper, we propose a new adap-tive approach for linear quadratic discrete-time games, in-cluding simultaneous and sequential games, with scalar in-puts and state feedback Nash strategies. We consider the

CT07 Abstracts 41

effort of adaptation under a Fictitious Play (FP) frame-work with learning algorithms derived from conventionaladaptive control methods. Convergence to Nash strate-gies is proved with the condition that there exists a uniquestate feedback strategy, which implies that the associatedcoupled discrete-time algebraic Riccati equations (DAREs)have a unique positive semi-definite solution. Piece-wiselinearization is used to transform general high level infor-mation fusion problems to linear quadratic discrete-timegames.

Genshe ChenIntelligent Automation, Inc.Senior Research Scientistgchen@i-a-i.com

MS5

Game Theoretic Sensor Resource Management forHigh-Level Distributed Fusion

We present a hierarchical game-theoretic approach to level2 and level 3 fusion problems. Given level 1 data of observa-tions of individual objects and prior knowledge of the com-position of enemy grouping, we consider the level 2 problemby developing a Bayesian inference algorithm for determin-ing the enemy identity. We then apply game theory towardthe level 3 problem, inferring the intent of enemy groups,given the determined identities and prior knowledge of en-emy strategies.

Sang ChinSAICPrincipal Scientistshc@alum.mit.edu

MS5

Disturbance Attenuation Analysis of SequentialGames in High Level Data Fusion

Recently, there have been increasing needs for research ingame theoretic approaches for high level information fu-sion. In this paper, we use a zero-sum game theoretical ap-proach to address the robust disturbance attenuation anal-ysis of state feedback Nash strategies for Dynamic LinearQuadratic Sequential Games (LQSGs) with uncertaintiesor disturbances. For finite-horizon LQSGs, we first providestate feedback Nash strategies with optimal attenuationlevels. Then we extend the approach to infinite-horizonLQSGs. We prove that the feedback system is BoundedInput Bounded Output (BIBO) stable with respect to thedisturbances. For the general dynamic games for high levelinformation fusion, piece-wise linearization is carried out totransform them to linear quadratic discrete-time games.

Jose CruzThe Ohio State UniversityDistinguised Professorcruz.22@osu.edu

MS5

Cooperative Outcomes for Stochastic Multi-PlayerNash Games: Performance-Measure Statistics andState-Feedback Paradigm

Recent theory of cost cumulant control has been used suc-cessfully in the area of stochastic regulator problems withnontrivial structural control benchmarks. Since optimalstochastic regulator problems can be seen as the one-playerspecial case of stochastic differential games, it is interesting

to explore the idea of applying this new control paradigmto the linear-quadratic class of nonzero-sum stochastic dif-ferential games where there are more than two playersand each player tries to minimize his individual perfor-mance measure. The utility of this newly developed con-trol paradigm can be applied to multi-person and multi-decision objective problems. For instance, a dynamic sen-sor allocation can be cast into a stochastic multi-playerNash game where multiple players are sensors. In this set-ting, each sensor has ability to selfishly seek to optimize itsown local objective. As a result, one can guarantee thatthe sensors will collectively operate efficiently.

Khanh D. PhamThe Air Force Research LaboratorySpace Vehicles Directoratekhanh.pham@kirtland.af.mil

MS6

Optimal Control of Mixed Immunotherapy andChemotherapy of Tumors

Abstract not available at time of publication.

Craig CollinsMurray State Universitycraig.collins@murraystate.edu

MS6

Parameter Estimation for a Model of BaroreflexRegulation of Heart Rate

The baroreflex is an important homeostatic mechanism ofthe cardiovascular system. Its purpose is to control andmaintain blood pressure by regulating heart rate, partic-ularly during orthostatic stress (i.e. sitting or standing).In this talk, we will give a basic outline of a mathematicalmodel that was designed to predict the dynamics of heartrate regulation with respect to postural changes from sit-ting to standing (Olufsen et al.). We will describe the pro-cess of calibrating the unknown parameters of this modelusing experimental data. In addition, we will include somesensitivity analysis results that lend some insight into themechanism and its predictive capabilities.

Katie FowlerClarkson Universitykfowler@clarkson.edu

Genetha GraySandia National Laboratoriesgagray@sandia.gov

MS6

Title Not Available at Time of Publication.

Abstract not available at time of publication.

Weiqing GuHarvey Mudd Collegegu@hmc.edu

MS6

A Mathematical Model Separates Quantitativelythe Cytostatic and Cytotoxic Effects of a HER2Tyrosine Kinase Inhibitor

Oncogene signaling deregulates cell proliferation resulting

42 CT07 Abstracts

in uncontrolled growth. Amplification and mutations ofthe HER2 proto-oncogene occur in approximately 20%of breast cancers. A therapeutic strategy that blocksHER2 function is the kinase inhibitor lapatinib. We de-termined experimentally the anti-proliferative effect of la-patinib combined with a mathematical model to interpretthe data. The model suggests that lapatinib acts by slow-ing the transition through G1 phase whle we also find apreviously unreported late cytotoxic effect.

Peter HinowVanderbilt Universitypeter.hinow@Vanderbilt.Edu

Shizhen WangDepartment of Cancer BiologyVanderbilt Universityemily.wang@vanderbilt.edu

Glenn F. WebbMathematics Department, Vanderbilt UniversityNashvilleglenn.f.webb@vanderbilt.edu

Carlos ArteagaDepartment of Cancer BiologyVanderbilt Universitycarlos.arteaga@vanderbilt.edu

MS7

Fast Solution of Nonlinear Optimal Control Prob-lems

We discus a class of optimization algorithms for nonlinearoptimal control problems. The optimization algorithmsare based on the all-at-once approach, use interior-pointtechniques for handling of classes of inequality constraints,employ trust-region methods for globalization, and allowa rigorous integration of iterative linear system solversfor the approximate solution of optimization subproblems.We present theoretical convergence results. In addition,the numerical performance of these methods is illustratedon test problems in which optimization subproblems aresolved iteratively using multigrid or domain decompositionmethods.

Matthias HeinkenschlossRice UniversityDept of Comp and Applied Mathheinken@rice.edu

MS7

Regularization Approaches in State ConstrainedOptimal Control of PDEs

In this talk Moreau-Yosida-based as well as Lavrentiev-based regularization for state constrained optimal controlproblems for partial differential equations are considered.The regularization is necessary due to the poor Lagrangemultiplier regularity. We investigate convergence prop-erties w.r.t. the regularization parameter and introducepath-following methods for the numerical solution. For afixed parameter setting the proposed methods are mesh-independent and converge locally superlinearly (the latterin function space). The talk ends by a report on test runsincluding a comparison with interior point solvers.

Michael HintermuellerUniversity of Graz

Austriamichael.hintermueller@uni-graz.at

MS7

Fast Optimized Wavelet Methods for StationaryPDE-Constrained Control Problems

We employ wavelet methods for control problems con-strained by non-linear stationary PDEs. The emphasis isplaced on the fast numerical solution of the optimality con-ditions leading to a coupled system of PDEs. Optimizedwavelet discretizations allow to employ fast iterative so-lution schemes of optimal computational complexity withsmall absolute iteration numbers. We also demonstratehow to employ norm equivalences in terms of wavelet basesto evaluate Sobolev norms of any order as accurately aspossible.

Roland PabelUniversitat Bonnpabel@iam.uni-bonn.de

MS7

Semismooth Newton Method for an Optimal Con-trol Problem with Control and Mixed Control-State Constraints

A class of optimal control problems for a semilinearparabolic partial differential equation with control andmixed control-state constraints is considered. For thisproblem, a projection formula is derived that is equivalentto the necessary optimality conditions. As main result, thesuperlinear convergence of a semismooth Newton methodis shown. Moreover we show the numerical treatment andseveral numerical experiments.

Arnd RoeschJohann-Radon Institute (RICAM)Austriaarnd.roesch@oeaw.ac.at

Daniel WachsmuthTech Universitat BerlinDepartment of Mathematicswachsmut@math.tu-berlin.de

MS8

Higher-Order Optimality Conditions for Nonregu-lar Constrained Optimization Problems

We start with considering higher-order optimality condi-tions for nonregular optimization problems with equalityconstraints given in the operator form as F (x) = 0, whereF : X → Y is an operator between Banach spaces and theFrechet derivative F ′(x∗) is not onto. Then we present op-timality conditions for nonregular problems with inequal-ity constraints in finite dimensional spaces when the activeconstraint gradients are linearly dependent at the solutionof the problem.

Alexey Tret’yakovUniversity of Podlasie in Siedlce, Poland, andSystem Research Institute, Polish Academy of Sciencestret@ap.siedlce.pl

Olga A. BrezhnevaMiami Universitybrezhnoa@muohio.edu

CT07 Abstracts 43

MS8

Generalized Jacobians and the Variational Differ-ential Inclusion

In the nonsmooth Maximum Principle, the classical varia-tional equation is replaced by a differential inclusion whoseright-hand side is the Clarke Generalized Jacobian of thereference vectorfield with respect to the state. The solu-tions then lead to a compact (usually nonconvex) set oflinear maps which is a Warga derivate container of thereference flow map. We extend this result to more gen-eral ”generalized Jacobians” and more general concepts ofmultivalued differential.

Hector J. SussmannRutgers UniversityDepartment of Mathematicssussmann@math.rutgers.edu

MS8

A Sufficient Condition for Exact Penalty in Con-strained Optimization

We use the penalty approach in order to study constraintminimization problems in a Banach space with Lipschitzianconstraints. We discuss sufficient conditions for the exis-tence of the exact penalty.

Alexander J. ZaslavskiTechnion Israel Inst of TechDept of Mathematicsajzasl@techunix.technion.ac.il

MS8

New Generalized Jacobians in Infinite DimensionalOptimzation Problems

In this talk a concept of generalized Jacobians for Lipschitzfunctions defined on infinite dimensional spaces wil be in-troduced. This notion extends to the infinite dimensionalsetting Clarke’s generalized Jacobian which is defined forLipschitz functions over finite dimensional spaces. Severalproperties and calculus rules are presented.

Vera ZeidanMichigan State UniversityDepartment of Mathematicszeidan@math.msu.edu

MS9

Comparison of Full- and Reduced-Order Models forFeedback Control of Fluids

The feedback control of fluid flows using model reductiontechniques has been studied for the past decade. In thisstudy, we investigate the effectiveness of the proper orthog-onal decomposition (POD/Galerkin) and a controller re-duction approach. Numerical results comparing these pop-ular approaches with Riccati equation-based linear statefeedback for control past circular cylinders and over abackward-facing step will be presented.

Jeff BorggaardVirginia TechDepartment of Mathematicsjborggaard@vt.edu

MS9

On Global Controllability Properties of a Swim-ming Model in a Nonstationary Stokes Fluid

We study the motion capabilities (“straight line motion”and “turns”) of an abstract object consisting of several“narrow” rectangles, subsequently connected by elasticlinks, which “swims” (as opposed to “being pushed orpulled”) in the 2-D Stokes fluid. We assume that themeans by which we can affect the swimming process arethe change of spatial orientations of the aforementionedrectangles and the direction and strength of the rotationforces acting between them.

Alexander KhapalovWashington State UniversityDepartment of Mathematicskhapala@math.wsu.edu

MS9

Issues in Control of Viscoelastic Flows

The lecture will present recent results on controllability ofviscoelastic flows. Constitutive models are assumed to beof Maxwell or Jeffreys type. Both linear and nonlinear situ-ations are examined. In contrast to the analogous situationin elasticity or Newtonian fluid mechanics, the linear prob-lem is controllable only within a subspace, and thereforethe linear results give no insights regarding controllabilityin the nonlinear case. I shall review a number of specialcases which are accessible to analysis.

Michael RenardyMathematics DepartmentVirginia Techrenardym@math.vt.edu

MS9

Regularity of Weak Solutions to a System of FluidStructure Interaction

A 3D fluid-structure interaction model in which an elasticbody is fully immersed in a viscous incompressible fluid isstudied. The interaction is realized through an interface,i.e., the boundary of the elastic body.We establish exis-tence of global weak solutions to this nonlinear model offluid structure interaction. We also establish existence ofsmooth solutions in both two and three dimensions givenmore regular initial data satisfying natural compatibilityconditions on the interface. This is joint work with V.Barbu, I . Lasiecka and Z. Grujic.

Amjad Tuffaha, Zoran GrujicDepartment of MathematicsUniversity of Virginiaat8e@virginia.edu, zg7c@virginia.edu

MS10

Numerical Approximation of Pursuit-EvasionGames with State Constraints

We present a new convergence result for the convergence ofa dynamic programming scheme to the viscosity solution ofthe Isaacs equation related to pursuit-evasion games withstate constraints in Rn. We will also give some detailson the implementation of the approximation scheme andof the numerical synthesis of optimal controls. Finally,several tests on the classical tag-chase game in a court with

44 CT07 Abstracts

internal obstacles will be presented.

Emiliano CristianiDipartimento di MatematicaUniversita’ di Roma ”La Sapienza”cristiani@mat.uniroma1.it

Maurizio FalconeUniversit‘a di Roma “La Sapienza”, Italyfalcone@mat.uniroma1.it

MS10

Convergence for a Curse-of-Dimensionality-FreeMethod for HJB PDEs

Nonlinear, steady-sate HJB PDEs with Hamiltoniansformed by (or well-approximated by) pointwise maxima ofquadratic forms are considered. (This includes switchedlinear systems.) A recent development is the discovery ofnumerical methods for such PDEs, which are not subject tothe curse-of-dimensionality. These methods work throughan approximation of the associated (max-plus linear) semi-group as a max-plus sum of semigroups associated with lin-ear/quadratic problems. A convergence rate is obtained in-dicating the number of iterations required to obtain a givenerror (scaled by the norm squared) over the entire space.Neither the number of iterations or the the computationsper iterations are subject to the curse-of-dimensionality. Inparticular, the computational growth as a function of di-mension is at a cubic rate. There is a ”curse of complexity”which must be addressed. Nevertheless, these new methodsare of both theoretical and practical interest.

William M. McEneaneyDept. of Mechanical and Aerospace EngineeringUniversity of California, San Diegowmceneaney@ucsd.edu

MS10

Optimal Trajectory Solutions Using Higher OrderImplicit Integration and Nonlinear Programming

Implicit integration combined with modern nonlinear pro-gramming packages has proven to be an effective techniquefor trajectory optimization. To provide greater fidelityand robustness, enhanced procedures have been developed.General procedures are presented for implicit integrationschemes of arbitrary order, automatic variable scaling andgrid refinement.. Computation experiences applying andcomparing these methods to interplanetary spacecraft andaircraft problems are given. These procedures have demon-strated substantial improvements in integration accuracyand robust operations.

Stephen ParisThe Boeing Companystephen.w.paris@boeing.com

MS10

The Role of Convexity in Optimal Control Theory

We consider a variational problem of the form

min l(x(0)) +

∫ τ

0

L(x(t), dx/dt)dt

where the minimization is over the absolutely continuousarcs x(.) that satisfy x(τ) = ξ. This talk explores proper-ties of the Fully Convex Control (FCC) problem in which

both l(.) and L(., .) are convex, but possibly nonsmoothand extended real-valued. The strong convexity hypothe-ses make the problem somewhat special, but as will be ex-plained, the FCC formulation still covers Linear QuadraticRegulator and its extensions with hard control constraints.The FCC problem plays roughly the role that linear sys-tems enjoy in nonlinear systems theory, and we shall ex-plore this analogy by presenting a unifying theory of nec-essary and sufficient conditions, duality, and a Hamilton-Jacobi theory. New research results and directions will alsobe presented.

Peter WolenskiDept. of Math.LSUwolenski@math.lsu.edu

MS11

Hybrid Monolithic Shape Memory Alloy Actuators

Abstract not available at time of publication.

Robert GorbetUniversity of WaterlooR.Gorbet@ece.uwaterloo.ca

MS11

Robust Controller Design for Magnetostrictive Ac-tuators

Magnetostrictive materials have many advantages for usein micro- positioning devices, but are difficult to controldue to their hysteresis and other nonlinearities. These ma-terials are passive and this property is used to identify aclass of stabilizing controllers. A controller in this classthat optimizes tracking performance is found. The con-troller is evaluated experimentally. The use of a similarapproach for control of other smart materials is discussed.

Kirsten MorrisDept. of Applied MathematicsUniversity of Waterlookmorris@uwaterloo.ca

MS11

Perturbation Control Techniques for MagneticTransducers

Abstract not available at time of publication.

Ralph C. SmithNorth Carolina State UnivDept of Mathematics, CRSCrsmith@eos.ncsu.edu

MS11

Robust Adaptive Control of Conjugated PolymerActuators

Abstract not available at time of publication.

Xiaobo TanMichigan State Universityxbtan@msu.edu

MS12

LQG Balanced POD for Distributed Parameter

CT07 Abstracts 45

Systems

Developing reduced order models for use in design ofclosed-loop controllers has attracted much attention in thelast five to ten years. Methods such as proper orthogo-nal decomposition (POD), balanced truncation, and LQGbalancing have been applied with varying degrees of suc-cess. A method was recently proposed, termed BalancedProper Orthogonal Decomposition, where two of the reduc-tion techniques are combined to utilize positive attributesof each. POD is well-suited to developing a model fromexperimental or computational data. Balanced truncationpreserves system properties such as controllability and ob-servability. In this paper, we explore combining POD withLQG balanced truncation. The latter method preservesproperties of the solutions to the control and filter Riccatiequations. We report on the performance of this methodfor systems modeled by partial differential equations.

Belinda A. BattenOregon State UniversityDept. of Mechanical Eng.bbatten@engr.orst.edu

John SinglerOregon State UniversityDept. of Mechanical Engineeringjohn.singler@oregonstate.edu

MS12

Sensitivity Analysis for Sensor/Actuator Place-ment

This talk surveys some results for sensitivity analysis re-lated to sensor/actuator placement for control design insystems governed by partial differential equations. Whensensor or actuator placement is parametrized as part of thecontrol design problem, the regularity of the solutions tothe governing mathematical models should be carefully ex-amined prior to sensitivity calculations. When the param-eter of interest determines location of sensors or actuators,the resulting sensitivity equations suffer from a loss of reg-ularity as compared with that of the original PDE model.This can have serious consequences if black box approachesto sensitivity computations are used. Model problems thatillustrate some of these issues are discussed.

Lisa G. DavisMontana State Universitydavis@math.montana.edu

MS12

Optimal Damping Design: An Eigenvalue Sensitiv-ity Approach

We consider a sensitivity approach for the optimal absorp-tion design for damped elastic systems. These systems aregenerally represented by abstract wave equations with vari-able damping coefficients. Using the sensitivity equationof eigenvalues of the corresponding system generator, a so-lution method is developed and analyzed for determiningthe optimal design with respect to the design parameter.Based on such a solution method, approximation methodsare also developed for construction of the optimal design.Numerical examples are presented to demonstrate the fea-sibility of our proposed method.

Fariba FahrooAir Force Office of Scientific Research

fariba.fahroo@afosr.af.mil

MS12

Mesh Independence for a Newton-Based RiccatiSolver

We consider the convergence of the infinite dimensionalversion of the Kleinman-Newton algorithm for solving thealgebraic Riccati operator equation associated with the lin-ear quadratic regulator (LQR) problem. In particular, weestablish mesh independence for this algorithm. The im-portance of dual convergence and preservation of exponen-tial stability (POES) with regard to strong convergence ofthe functional gains and mesh independence of the algo-rithm are discussed. These results are applied to systemsgoverned by delay equations and numerical results are pre-sented using different approximation schemes.

Lizette ZietsmanVirginia TechBlacksburg, VA 24061-0123lzietsma@vt.edu

MS13

Feedback Stabilisation of Navier-Stokes System:Approximation and Error Estimates for the Ric-cati Approach

Errors estimates related to general approximation ofclosed-loop systems are provided. The feedback law inthe closed-loop system is expressed with the solution ofan infinite dimensional algebraic Riccati equation, whichis provided by an optimal control problem stated over aninfinite time horizon. The case of nonconform and semidis-crete approximation is investigated. We give examples ofapplications dealing with the closed-loop Oseen equations,where the feedback law is chosen so that it locally stabi-lizes, near a given steady-state flow, the solutions of theNavier-Stokes equations in a bounded domain.

Mehdi BadraUniversite Paul Sabatier Toulouse 331062 TOULOUSE cedex 9, Francebadra@mip.ups-tlse.fr

MS13

Optimal Control of Heat Transfer with Radia-tion Interface Conditions and Pointwise State-Constraints

The talk is concerned with an optimal control problemarising from the optimization of the temperature distri-bution within the sublimation growth of semiconductorsingle-crystals. The problem consists of a semilinear el-liptic partial differential equation with nonlocal radiationinterface conditions and pointwise control and state con-straints. First, the existence of a unique continuous solu-tion of the semilinear state equation is established. More-over, it is shown that the associated solution operator iscontinuously Frechet-differentiable. Based on this and thecontinuity of the solution, it is possible to establish theexistence of Lagrange mutlipliers in the space of regularBorel measures by means of the Karush-Kuhn-Tucker the-ory. Furthermore, the associated adjoint equation withthese measures as inhomogeneity is discussed. It is shownthat this equation admits a solution in W 1,q with someq < N/(N − 1), where N denotes the spacial dimension.This allows to establish necessary and sufficient optimal-

46 CT07 Abstracts

ity conditions. The theoretical results are illustrated bynumerical examples.

Christian MeyerWIAS, Berlinmeyer@wias-berlin.de

MS13

On the Finite Element Approximation of EllipticOptimal Control Problems with Neumann Bound-ary Control

A Neumann boundary control problem for a linear-quadratic elliptic optimal control problem in a convex andpolygonal domain is investigated. The main goal is to showan optimal approximation order for discretized problemsafter a postprocessing process. It turns out that two sat-uration processes occur: The regularity of the boundarydata of the adjoint is limited if the largest angle of the poly-gon is at least 2π/3. For piecewise linear finite elements,the theory cannot deliver optimal approximation rates forconvex domains. We will derive error estimates of order hσ

with σ ∈ [3/2, 2] depending on the largest angle and prop-erties of the finite elements. Moreover, we will investigatealso the case of domains with a reentrant corner. Here, weobtain error estimates of order hσ with σ ∈ [1, 3/2] Finally,numerical tests illustrate the theoretical results.

Mariano MateosUniversidad de OviedoSpainmmateos@orion.ciencas.uniovi.es

Arnd RoeschJohann-Radon Institute (RICAM)Austriaarnd.roesch@oeaw.ac.at

MS13

Homotopy Methods for State Constrained OptimalControl

We consider homotopy methods in function space for op-timal control problems subject to PDE constraints andbounds on the state. Our main focus here is on interiorpoint methods. We study structure and convergence of ho-motopy paths generated by logarithmic and rational bar-rier functions. It turns out that the proper type of barrierfunction has to be chosen in order to guaranty existenceand strict feasibility of solutions in function space. Then,for the right type of barrier functions, the convergence of aNewton path-following scheme to the solution of the origi-nal state constrained problem can be established.

Anton SchielaZIB, Berlinschiela@zib.de

MS14

Mangasarian-Fromowitz Assumptions and Opti-mality Conditions for Mixed Constrained Problems

The focus of this paper is on Mangasarian-Fromowitz typeconditions for mixed constrained optimal control problemswith possibly nonsmooth dynamics. We show how neces-sary conditions of optimality in the form of unmaximizedHamiltonian type conditions can be derived under such as-sumptions. The Unmaximized Hamiltonian inclusion type

conditions we obtain here are distinct from well knownversions of weak nonsmooth maximum principle becausethey employ a joint subdifferential instead of the custom-ary product of partial subdifferentials.

M. Do Rosario De PinhoFaculdade de Engenharia da Universidade do PortoDEECmrpinho@fe.up.pt

MS14

Optimality Conditions for Asymptotically StableControl Systems

We consider infinite horizon optimal impulsive controlproblems for which a performance criteria is minimizedby choosing asymptotically stable control strategies. Wepresent necessary optimality conditions in the form of max-imum principle and show how they can be derived froman auxiliary conventional (nonimpulsive) optimal controlproblem with mixed constraints. As far as we know, resultsof this kind have not been previously derived for problemswith trajectories restricted to the set of stabilizing ones.

Geraldo Nunes SilvaIBILCE, Universidade Estadual de S. Paulogsilva@ibilce.unesp.br

Fernando F. Lobo PereiraFaculadade de Engenharia da Universidade do PortoPorto, Portugalflp@fe.up.pt

MS14

Regularity Properties of Optimal Control forMixed Constrained Problems

In this paper we investigate regularity properties (Lipschitzcontinuity and differentiability) of the optimal control inlinear-quadratic problems with mixed control/state con-straints of equality and inequality type. It is shown thatunder appropriate hypotheses the optimal control possessesthe indicated regularity.

Ilya ShvartsmanMiami UniversityOxford, OHshvartia@muohio.edu

MS14

Invariance Properties for Impulsive Systems

This talk will consider a dynamical system in which therighthand side contains a measure with state-dependentcoefficients. A solution concept that involves a graph com-pletion will be introduced, and characterizations of the sys-tem’s weak and strong invariance properties will be pro-vided.

Peter WolenskiDept. of Math.LSUwolenski@math.lsu.edu

MS15

Structure of Solutions for Ergodic Type Bellman

CT07 Abstracts 47

Equations of First Order

Ergodic type Bellman equations of first order with aquadratic Hamiltonian are considered in the framework ofviscosity solutions. It is known that the equations havemultiple solutions even if the solutions are identified un-der additive constants. We will show that there exists acritical solution. We will also deduce the min-max typerepresentation for the critical value, which is motivatedfrom Donsker-Varadhan min-max formula of the principaleigenvalue for the second order linear differential operators.

Hidehiro KaiseDept. of MathematicsNagoya UniversityEmaikaise@is.nagoya-u.ac.jpl

MS15

Max-Plus Integral Kernels and a Fundamental So-lution for Differential Riccati Equations

The semigroups associated with Bellman equations aremax-plus linear. The semigroup operators have semiconvexdual operators with representations as max-plus integraloperators. In the linear-quadratic case, the kernel of thesemiconvex dual operator is a quadratic function. Prop-agation in the dual space is through composition of theseoperators, and hence max-plus integral convolutions. Thisleads to a surprising new understanding of Riccati equa-tions where the quadratic term is sign-definite, and a newfundamental solution for them. This fundamental solutionhas a very nice control interpretation, and so leads to amore satisfying understanding of Riccati equations.

William M. McEneaneyDept. of Mechanical and Aerospace EngineeringUniversity of California, San Diegowmceneaney@ucsd.edu

MS15

Aronsson Equation and Deterministic OptimalControl

Aronsson equation is a second order degenerate ellipticequation that appears in L∞ minimization problems and issatisfied by the so called absolute minimizers. We will dis-cuss the fact that value functions in deterministic optimalcontrol are absolute minimizers in regions where they arebilateral viscosity solutions of the classical Bellman equa-tion. We will then derive Aronsson equation for value func-tions under weaker assumptions than the standard theory.

Pierpaolo SoraviaUniversity of PadovaDept of Pure & Applied Mathsoravia@math.unipd.it

MS15

An Overview of the Applications of Game Theoryto Importance Sampling

Importance sampling (IS) algorithms for estimating rare-event probabilities are intimately connected with two-person zero-sum differential games. This game interpre-tation shows that state-dependent schemes are needed inorder to attain asymptotic optimality in a general setting.We show that the classical subsolutions of the associatedIsaacs equation can be used as a basic and flexible tool forthe construction and analysis of efficient IS schemes. We

also present some numerical examples of rare event simu-lation in queueing networks.

Hui WangBrown Universityhuiwang@cfm.brown.edu

MS16

Closed-loop Control of Channel Flow Using Bal-anced Proper Orthogonal Decomposition

Reduced-order models of linearized channel flow obtainedusing balanced proper orthogonal decomposition (BPOD),a close numerical approximation to balanced truncation,are used to develop optimal closed-loop controllers. Themodels are better at capturing the input-output behaviorof the system compared to standard POD/Galerkin mod-els. We use these models to design closed-loop controllersto suppress transition to turbulence in channel flow, usingbody forces and wall blowing/suction for actuation.

Milos Ilak, Clarence W. RowleyPrinceton Universitymilak@princeton.edu, cwrowley@princeton.edu

MS16

Model Reduction of Nonlinear Control Systems

We review methods for model reduction for linear and non-linear control systems and offer a new method for nonlinearcontrol systems. We also present new error estimates forboth linear and nonlinear model reduction.

Arthur J. KrenerUniversity of CaliforniaDepartment of Mathematicsajkrener@ucdavis.edu

MS16

Cross Gramians and Riccatians for ApproximateBalancing of Nonlinear Systems

Abstract not available at time of publication.

Jacquelien ScherpenDelft Center for Systems and ControlDelft University of Technologyj.m.a.scherpen@dcsc.tudelft.nl

MS16

Nonlinear Balanced Realizations

Abstract not available at time of publication.

Erik VerriestSchool of Electrical and Computer EngineeringGeorgia Institute of Technologyerik.verriest@ece.gatech.edu

MS17

Multigrid Algorithms for Distributed ParameterEstimation Problems

Here I consider distributed parameter estimation relatedto the inverse medium problem for elliptic, parabolic, andhyperbolic PDEs. In this talk I will present three repre-sentative examples, for a Helmholtz, a reaction-diffusion,

48 CT07 Abstracts

and an acoustic wave propagation PDE. I will present theinverse operator, and discuss the spectral properties. I willconclude with a list of recently proposed multilevel algo-rithms that are robust as the regularization is reduced,achieve optimal algorithmic complexity, and can scale toparallel computing architectures.

George BirosUniversity of Pennsylvaniabiros@seas.upenn.edu

MS17

Towards an Optimal Control Approach for Drink-ing Water Decontamination

When a drinking water network is contaminated, harm-ful particles and chemicals in the fluid may be transportedinto biofilms present on pipe surfaces. Effective decontam-ination of a system with biofilms is not well understood.We will discuss an approach for removing contaminants inbiofilms by controlling the fluid flow profile. Our controlmethodology makes use of a multiscale and multi-physicsmodel of a biofilm coupled to a continuum model for fluidflow.

Bart G. Van Bloemen Waanders, Judith HillSandia National Laboratoriesbartv@sandia.gov, jhill@sandia.gov

MS17

Inexact Null-Space Iterations in PDE-ConstrainedOptimization

Upon discretization, PDE-constrained minimization prob-lems lead to large scale finite dimensional mathematicalprograms. In this talk, we focus on preconditioned iter-ative solvers for such optimization problems. The solverconcept is based on user chosen iterative forward and ad-joint solvers, which might be only linearly convergent andwhich are intertwined with a suitable preconditioner for theoverall KKT-system. Every step of the algorithm can bedecomposed into feasibility restoration (null space restora-tion) and a step towards optimality. An exact L1-meritfunction operates as a progress measure. A convergenceanalysis is presented and a report on numerical tests isgiven.

Michael HintermuellerUniversity of GrazAustriamichael.hintermueller@uni-graz.at

MS17

Optimal Control and Model Reduction of PDAEFuel Cell Models

Molten carbonate fuel cells (MCFC) are especially wellsuited for stationary power plants if their process heat isused to increase their efficiency. MCFCs will become sooncompetitive compared with traditional power plants. Thedynamic behaviour of MCFCs is governed by effects fromgas dynamics, electrochemical reactions, electrodynamicsand heat transfer. These effects can be modelled mathe-matically by a hierarchy of systems of partial differential al-gebraic equations (PDAE) in 1D or 2D of mixed parabolic-hyperbolic type. Integral terms appear and the nonlinearboundary conditions are given partly by a DAE system.These large PDAE systems of dimension between roughly10 and 30 equations are discretized by the method of lines,

yielding huge dimensional DAEs. In order to enable realtime control of the system model reduction techniques areneeded. We choose the snapshot form of proper orthogo-nal decomposition (POD). We will present new computa-tionally expensive numerical results of (sub)optimal controlduring load changes for a 2D dynamical MCFC model.

Hans Josef PeschUniversity of Bayreuth, GermanyChair of Mathematics in Engineering Scienceshans-josef.pesch@uni-bayreuth.de

Armin RundUniversity of Bayreuth,Department of Mathematicsarmin.rund@uni-bayreuth.de

MS18

Scalable Nonlinear Multigrid Solvers for InverseReaction-Diffusion Problems

In this talk we present multigrid smoothers for saddle-pointEuler Lagrange equations related to inverse problems forsystems governed by parabolic PDEs. Due to the problemsize of these problems, we have to devise matrix-free pre-conditioners. Due to the ill-conditioning, efficient multigridsolvers are required. The two key components of multi-grid are the intergrid transfer operators, and the smoother.Here we restrict our attention to construction of efficientsmoothers for full-space formulations of the inverse prob-lem.

George Biros, Santi S. AdavaniUniversity of Pennsylvaniabiros@seas.upenn.edu, adavani@seas.upenn.edu

MS18

Multilevel Optimization Methods for the Controlof the Transport of Bose-Einstein Condensates

The optimal control of the transport of Bose-Einstein con-densates in magnetic microtraps is formulated and solvedefficiently by multilevel optimization schemes. The timeevolution of the wavefunction of the Bose-Einstein conden-sates is governed by the Gross–Pitaevskii equation. Thiswavefunction is manipulated through variation of a con-trollable magnetic confinement potential and an efficientcontrol strategy for this potential is determined within theframework of optimal control theory. To solve the resultingproblem a cascadic nonlinear conjugate gradient schemeand a full multilevel optimization scheme are considered.For a variety of magnetic confinement potentials we studytransport and wavefunction splitting of the condensate,and demonstrate that the optimal control theory approachallows to drastically outperform more simple schemes forthe time variation of the microtrap control parameters.

Alfio BorziUniversity of GrazInstitute for Math and Scientific Computingalfio.borzi@uni-graz.at

MS18

Adaptive Finite Elements for Parabolic Optimiza-tion Problems

In this talk we present a posteriori error estimates forspace-time finite element discretizations of parabolic op-

CT07 Abstracts 49

timization problems developed in (D. Meidner and B.Vexler, Adaptive Space-Time Finite Element Methods forParabolic Optimization Problems, to appear in SIAM J.Control Optim.). The provided error estimates assess thediscretization error with respect to a given quantity ofinterest and separate the influences of different parts ofthe discretization (time, space, and control discretization).This allows to set up an efficient adaptive algorithm whichsuccessively improves the accuracy of the computed solu-tion by construction of economical, locally refined meshesfor each time step separately and of an adaptive time dis-cretization. Numerical examples for nonlinear parabolicequations confirm the efficiency of our method.

Boris VexlerRICAM, Austrian Academy of Sciencesboris.vexler@oeaw.ac.at

Dominik MeidnerUniversity of Heidelberg, Germanydominik.meidner@iwr.uni-heidelberg.de

MS19

Riccati Synthesis for Structural Acoustic ControlProblems

In this talk, we will discuss the feasibility of numericallyapproximating the minimal norm steering control, relativeto the boundary null controllability of a structural acousticinteraction. This approximation of the optimal null controlwill be the result of a numerical analysis of the appropriateRiccati Equation. Results of convergence for approxima-tions of both the null controller and the corresponding dy-namics will be presented. This is joint work with MichaelGunderson.

George AvalosUniversity of Nebraska-LincolnDepartment of Mathematics and Statisticsgavalos@math.unl.edu

MS19

Hamiltonian Based Riccati Theory and Fast RiccatiSolver

We develop a fast algorithm to compute the optimal feed-back gain for the linear quadratic regulator problem. Thealgorithm utilizes the relation between an invariant sub-space of the corresponding Hamiltonian operator and thesolution to the Riccati equation and is based on the inverseof the Hamiltonian operator. Large scale control systemsthat arise from a discretization of a class of control prob-lems governed by partial differential equations is used todemonstrate the feasibility and applicability of Algorithm.A sparsity and structural property of system matrices areincorporated in Algorithm and it enables us to compute astabilizing feedback law for very large control systems.

Kazufumi ItoNorth Carolina State UniversityDepartment of Mathematicskito@math.ncsu.edu

MS19

Controller Design for Infinite-Dimensional Systems

There are essentially two approaches to controller design

for systems modelled by partial differential equations. Inthe first approach, the full model of the system is usedin controller design. The designed controller is generallyinfinite-dimensional and is often subsequently reduced be-fore implementation. This is known as direct controllerdesign. In the second approach, indirect controller design,the model is reduced to obtain a finite-dimensional model.This finite-dimensional approximation is used for controllerdesign. Both approaches will be examined in the context ofseveral models for acoustic noise. The models vary in com-plexity and in how different aspects of the dynamics aremodelled. The modelling has consequences has controllerdesign.

Kirsten MorrisDept. of Applied MathematicsUniversity of Waterlookmorris@uwaterloo.ca

MS19

On Sampled-Data Controller Implementation forSpatially Distributed Systems

Consider a linear, infinite-dimensional, exponentially sta-ble plant which has impulse response given by a matrix-valued Borel measure. Let r(t) be a vector-valued refer-ence signal which is the linear combination of finitely manyknown sinusoidals, but otherwise unknown. Suppose thesystem is subject to disturbances which are asymptotic tofinite sums of sinusoidals. We design a low-gain sampled-data controller which maintains the stability of closed-loopsystem and approximately tracks r(t).

Richard L. RebarberUniversity of Nebraskarrebarber1@math.unl.edu

Hitay OzbayBilkent University, Turkeyozbay@ece.osu.edu

MS20

Progressive Strategies for Differential Games

Two controller, zero sum differential games on a fixed fi-nite time horizon are considered. A lower game value isdefined using strategies which depend in a progressivelymeasurable way on past control choices for the maximizer.Results about viscosity solutions of the Isaacs PDE im-ply that this lower value function is the same as with theElliott-Kalton definition. With a smaller class of ”strictlyprogressive” strategies for the minimizing controller, theupper value is obtained instead of the lower value.

Wendell FlemingDivision of Applied MathematicsBrown Univ.whf@cfm.brown.edu

MS20

Numerical Methods for Regime-Switching Stochas-tic Differential Games

This work is concerned with numerical methods forstochastic differential games of regime-switching diffusions.Procedures based on Markov chain approximation tech-niques are developed. A new proof of the existence of a sad-dle point for the stochastic differential game is presented,

50 CT07 Abstracts

which enables us to treat certain systems with nonsepara-ble (in controls) cases. Convergence of the algorithms isderived by weak convergence methods. In addition, exam-ples are also provided for demonstration.

George G. YinWayne State UniversityDepartment of Mathematicsgyin@math.wayne.edu

Qingshuo Songuniversity of southern californiaqingshus@usc.edu

MS20

Liapunov-Like Sufficient Conditions for the Guar-anteed Capture or Evasion in Multi-Player Differ-ential Games

In this presentation, two sequences of continuously differen-tiable functions that represent convergent approximationsof the min and the max function, respectively, are con-sidered. Using these functions we design pursuers’ andevaders’ strategies that guarantee either capture or eva-sion of the evaders. These strategies are proven to achievethe corresponding goals using a Liapunov-like methodol-ogy. Dynamic models for the agents are assumed to benonlinear which is particularly important if the agents rep-resent vehicles.

Dusan M. StipanovicIndustrial and Enterprise Sys. Eng.Univ. of Illinois at Urbana-Champaigndusan@uiuc.edu

Arik MelikyanRussian Academy of Sciencesmelik@ipmnet.ru

Naira HovakimyanVirginia Technhovakim@vt.edu

MS21

Model Order Reduction of Truly Large-Scale RCLNetworks

Abstract not available at time of publication.

Roland W. FreundUniversity of California, DavisDepartment of Mathematicsfreund@math.ucdavis.edu

MS21

A Proper Orthogonal Decomposition Approach forthe Empirical Balancing of Nonlinear Systems withUnstable Linearization

Abstract not available at time of publication.

Boumediene HamziDepartment of Mathematics, UCDavis.hamzi@math.ucdavis.edu

MS21

Optimal H2 Model Reduction of MIMO Systems

Abstract not available at time of publication.

Andrew MayoDepartment of Electrical and Computer EngineeringRice Universityajmayo@hoss.ece.rice.edu

MS21

Balancing for Infinite-Dimensional Linear Systems

We show that balancing methods can be generalized toinfinite-dimensional linear systems. This is true for theusual Hankel-balancing, but also for variants such as LQG,H-infinity, bounded real and positive real balancing. Theknown error-bounds generalize to the infinite-dimensionalcase. However, the upperbound may now be infinite. Wegive conditions under which the upperbound is finite andone thus obtains convergence of finite-dimensional approx-imants in the desired metric.

Mark R. OpmeerDepartment of MathematicsUniversity of California Davismropmeer@ucdavis.edu

MS22

Path-Following Primal-Dual Interior-Point Meth-ods for Shape Optimization of Stokes Flow Prob-lems

We are concerned with shape optimization problems inchannel fluid flow problems. The state variables are sup-posed to satisfy the Stokes system and the design vari-ables are the control points of a Bezier curve representingthe geometry of the channel subject to bilateral pointwiseconstraints. Within a primal-dual setting, we suggest anall-at-once approach based on interior-point methods. Theresulting parameter dependent nonlinear system is solvedby an adaptive path-following technique within the frame-work of an affine invariant convergence theory. The dis-cretization is taken care of by Taylor-Hood elements withrespect to a simplicial triangulation of the computationaldomain and automatic differentiation is used in the com-putation of first and second order derivatives. Numericalresults illustrate the convergence behaviour of the adpativepath-following interior-point method.

Harbir AntilUniversity of Houston,Department of Mathematicsharbir@math.uh.edu

Ronald H.W. Hoppe, Christopher LinsenmannUniversity of HoustonDepartment of Mathematicsrohop@math.uh.edu, linsen@math.uh.edu

MS22

Multiscale Optimization of Gas Networks

We are interested in gas flow in pipe networks. Severalmodels for the dynamics inside the pipe are known whichrange from partial differential equations to purely algebraicrelations. Usually, the dynamics of different pipes is cou-pled at pipe fittings and we discuss the mathematical and

CT07 Abstracts 51

physical reasonable coupling conditions in particular fornodes which model compressors. These nodes can be con-trolled by prescribing the applied compressor energy. Weare interested in questions of well-posedness and existenceof solutions and discuss optimization techniques relying onthe given model hierarchy. Finally, we present numericaloptimization results for sample networks.

Michael HertyUniversity of Kaiserslautern,Department of Mathematicsherty@mathematik.uni-kl.de

MS22

Path-Following Methods for a Class of MPCCs inFunction Space

We consider Mathematical Programs with Complementar-ity Constraints in function space. Typical model problemsare related to optimal control of variational inequalities(VIs) or parameter identification in VIs. Here we proposea relaxed Moreau-Yosida based path-following concept forthe development of a first order optimality characteriza-tion as well as the design of a solution algorithm. Our firstorder conditions are close to strong stationarity in finitedimensions. The proposed algorithm uses a semismoothNewton method (with a locally superlinear convergence infunction space) for solving the relaxed path-problems. Thetalk ends by a report on numerical tests.

Ian KopackaUniversity of Graz,START-Project Interfaces and Free Boundariesian.kopacka@uni-graz.at

Michael HintermuellerUniversity of GrazAustriamichael.hintermueller@uni-graz.at

MS22

Model Reduction in Laser Welding

Laser welding is a modern joining technique for new metal-lic materials particularly aluminum alloys. However, thereis a high risk of hot cracking. Therefore, the aim is toavoid this undesirable effect caused by several processesduring the solidification. For modelling process there arethree main aspects which have to be considered: The ther-modynamical, the mechanical and the metallurgical effectby which the arising of the opening displacement causedby transverse tensile strains can be described. Because ofthe high complexity of this physical process a model reduc-tion in the mathematical model has to be done. After thatformulation a method can now be applied to prevent hotcracking. One possibility is to use the so called multi-beamtechnique. Thereby, additional laser beams are imposedto compensate for the strain induced by the main laserbeam. Hereby, it is important to determine the optimalposition, size and power of the additional laser beams in or-der to prevent hot cracking. Mathematically, this leads to aconstraint nonlinear optimization problem where amongstother constraints a partial differential equation has to besolved.

Verena PetzetChair of Mathematics in Engineering SciencesUniversity of Bayreuthverena.petzet@uni-bayreuth.de

Hans Josef PeschUniversity of Bayreuth, GermanyChair of Mathematics in Engineering Scienceshans-josef.pesch@uni-bayreuth.de

MS23

State and Output Feedback Control over PacketDropping Network Links

We study a stabilization scheme for a discrete-time con-trol system in which the feedback loop includes a networklink that may suffer packet drops. We study state/outputfeedback stabilization schemes for linear systems of arbi-trary dimension. We also compare it against an alterna-tive control scheme that first uses Kalman filtering (withintermittent observations) to estimate the state and thenapplies state feedback based on this state estimate. Weconclude that, under certain conditions, the two controlschemes can have comparable performance but the pro-posed state/output feedback strategy is considerably sim-pler to implement.

Christoforos N. Hadjicostis, Haitao MoCoordinated Science LaboratoryUniversity of Illinois at Urbana-Champaignchadjic@control.csl.uiuc.edu, hmo2@uiuc.edu

MS23

A Real-Time Distributed Priority-Based Protocolfor CAN Networks based on Delay Impulsive Sys-tems

We consider Networked Control Systems (NCSs) consist-ing of a LTI plant; a linear static or dynamic feedback con-troller; a collection of sensors that provide measurements tothe controller; and a collection of actuators that are used tocontrol the plant. The different elements of the control sys-tem are spatially distributed, but interconnected througha communication network. Due to the shared and unreli-able channel used to connect the subsystems, the samplingintervals are uncertain and variable. Moreover, samplesmay be dropped and experience uncertain and variable de-lays before arriving at the destination. We show that theresulting NCSs can be viewed as a MIMO sampled-datasystem with variable sampling intervals and delay, whichcan be modeled by delay impulsive systems. We provideconditions for the stability of the closed-loop expressed interms of LMIs. By solving these LMIs, one can determinepositive constants that determine upper bounds betweenthe sampling time and the next update time at the des-tination, for which stability of the closed-loop system isguaranteed. Based these results, we present a schedulingtest based on Earlier Deadline First (EDF) algorithm forreal-time systems. If the test passes, the stability of severalcontrol systems sharing a network is guaranteed. Then wepresent a Medium Access Control (MAC) protocol whichcan be implemented on Controller Area Networks (CAN)in real-time and in a distributed fashion which grants theaccess to the network to a node with the earliest deadline.

Payam NaghshtabriziUniv. of California, Santa BarbaraDepartment of Elec. & Comp.payam@ece.ucsb.edu

Joao HespanhaUniv. of California, Santa BarabaraElectrical and Computer Engineeringhespanha@ece.ucsb.edu

52 CT07 Abstracts

MS23

Distributed Sensor Pre-Processing for FeedbackStabilization, In the Presence of Unreliable Inter-connections

Consider an unstable discrete-time, linear and time-invariant plant, two sensors, with computational capabil-ities, and one controller. Each sensor collects noisy mea-surements of a linear combination of the state of the plant.This paper addresses the design of the controller and of theprocessing at the sensors so as to stabilize the plant. Thesensors are connected to the controller via two stochasticlinks whose connectivity is modeled by two independentBernouli processes, with loss probabilities p1 and p2. Weshow that it is a necessary and sufficient condition for sta-bility that the pair (-log(p1),-log(p2)) lies in a two dimen-sional convex region, which is uniquely determined by theparameters of the plant.

Vijay GuptaUniversity of MarylandCollege Parkvijay@cds.caltech.edu

John BarasUniv. MarylandCollege Parkbaras@umd.edu

Nuno C. MartinsUniversity of Maryland at College Parknmartins@umd.edu

MS23

Feedback Control over Signal to Noise Ratio Con-strained Communication Channels

Recently, there has been growing interest in stabilisabilityand performance problems in control over communicationchannels. Here we present an overview of recent resultswhen a signal-to-noise ratio (SNR) constrained channel isconsidered. We discuss the linear time invariant (LTI) out-put feedback discrete-time case. Our analysis closely par-allels results in bit rate limited control. The SNR frame-work used enables LTI stability, robustness, performanceand delay analysis.

Julio Braslavsky, Alejandro J. Rojas, Richard MiddletonThe University of Newcastlejulio.braslavsky@newcastle.edu.au,Alejandro.Rojas@studentmail.newcastle.edu.au,richard.middleton@newcastle.edu.au

MS24

Robust Quantum Potential Profile Design for Elec-tron Transmission

Abstract not available at time of publication.

Robert KosutSC Solutionskosut@scsolutions.com

MS24

Robust Design of Slow-Light Tapers in Periodic

Waveguides

Abstract not available at time of publication.

Almir MutapcicStanford Universityalmirm@stanford.edu

Stephen BoydStanford UniversityDepartment of Electrical Engineeringboyd@stanford.edu

MS24

Robust Optimization in Electromagnetics

Abstract not available at time of publication.

Dimitris BertsimasMassachusetts Insitute of Technologydbertsim@mit.edu

Omid NohadaniMassachusetts Institute of Technologynohadani@mit.edu

MS24

Non-Intuitive Design of Negative Refractive Indexand Nano-Scale Electronic Devices

Optimal design is used to show that electromagnetic res-onators with almost uniform field intensity and up to twicethe energy density of conventional structures are possibleby exploiting the properties of negative refractive indexmaterials. Efficient computation and local optimization isachieved by solving the underlying PDE on an unboundeddomain and the adjoint method to efficiently compute thegradient of the cost functional with respect to design pa-rameters. The same method has also been applied to nano-scale electronic device design.

Philip SeligerUniversity of Southern Californiaseliger@usc.edu

A.F.J. LeviUniversity of Southern CaliforniaDepartment of Electrical Engineering-Electrophysicsalevi@usc.edu

Chunming WangDepartment of MathematicsUniversity of Southern Californiacwang@math.usc.edu

Gary RosenUniversity of Southern CaliforniaApplied Mathematicsgrosen@math.usc.edu

MS25

Combinatorial Motion Planning of Multi-VehicleSystems

In this talk, I will consider the problem of motion planningfor vehicles with a constraint on the minimum turning ra-dius. The motion planning problem is as follows: Given aset of n targets to visit, m vehicles that start at distinct lo-

CT07 Abstracts 53

cations (depots), choose at most p ≤ m vehicles and theircorresponding tours so that (1) each target is visited byat least one vehicle and (2)the total distance travelled bythe collection is a minimum among all possible choices ofvehicles and their tours. By a tour, one must find not onlythe sequence of targets to be visited by the vehicle butalso the angle at which it must be visited. I will presentapproximate algorithms based on a two step procedure: Inthe first step, the combinatorial problem is solved based onthe Euclidean distances between the targets and the sec-ond step is to find the heading angles at the targets usinga dynamic programming approach.

Swaroop DarbhaTexas A&M University at College Stationdswaroop@mengr.tamu.edu

MS25

Value Function Based Control of Sensing Opera-tions

The problem of tasking sensing assets when little prior in-formation is known is very challenging. In such situations,one must clearly keep in mind that the value of informa-tion is in its ability to help win the battle. In this paper,we present a game-theoretic approach to designing sensingplans in order to maximize success of the overall battleplan.Dynamic programming provides means of determining op-timal sensing courses of action.

Ben G. Fitzpatrick, Yun WangTempest Technologiesfitzpatrick@tempest-tech.com, wang@tempest-tech.com

MS25

Title Not Available at Time of Publication

Abstract not available at time of Publication.

Vikram KrishnamurthyUniversity of British ColumbiaDepartment of Electrical and Computer Engineeringvikramk@ece.ubc.ca

MS25

Real-Time Optimal Motion Planning for Un-manned Vehicles

Abstract not available at time of publication.

I. Michael RossNaval Postgraduate Schoolimross@nps.navy.mil

MS26

The LaxFriedrichs Sweeping Method for OptimalControl Problems in Continuous and Hybrid Dy-namics

Assuming that the Hamiltonian is strictly convex in thecontrol variable, we derive a pair of HJ equations in con-tinuous time through the dynamic programming formula-tion. The LaxFriedrichs sweeping (LFS) method is appliedto solve the coupled PDEs by successive iteration of theoptimal cost and control. The method also applies to opti-mal control problems in hybrid systems. We demonstratethe efficiency of the method through numerical examples

in both continuous and hybrid dynamics.

Chiu-Yen KaoDept. of MathematicsOhio State Universitykao@math.ohio-state.edu

MS26

PDEs in Control Theory

We review the important PDEs that arise in nonlinear con-trol theory and methods for solving them.

Arthur J. KrenerUniversity of CaliforniaDepartment of Mathematicsajkrener@ucdavis.edu

MS26

Numerical Method for Hamilton-Jacobi-BellmanEquations in High Dimension

We present a novel method for solving the Hamilton-Jacobi-Bellman PDE arising in optimal control problemsin high dimension. First the HJB PDE is solved locallyusing Albrecht’s power series method. Then power seriessolutions of the HJB PDE outside the local neighborhoodare patched together. For each power series solutions, wesolve a Cauchy problem where the boundary conditions arethe Cauchy data defined on a noncharacteristic surface ofthe PDE.

Carmeliza L. NavascaETIS Lab, CNRS, Francenavasca@ensea.fr

MS26

A New Discontinuous Galerkin Method for Di-rectly Solving Hamilton-Jacobi Equations

Different to Hu-Shu’s paper in 1999, we propose a directdiscontinuous Galerkin method to solve Hamilton-Jacobiequations. For the linear case, the method is equivalent tothe discontinuous Galerkin method for conservation laws.Thus, stability and error analysis are valid. For both con-vex and nonconvex Hamiltonians, optimal (k+1)-th orderof accuracy for smooth solutions are obtained with piece-wise k-th polynomial approximations. The schemes arenumerically tested on a variety of one and two dimensionalproblems. The method works well to capture sharp cor-ners(discontinuous derivatives) and converges to the vis-cosity solution.

Jue YanDept. of MathematicsIowa State Universityjyan@iastate.edu

MS27

Military Applications and Sensitivity Analysis ofCoupling Game

Coupling game theory can formulate some non-ideal gamecases and provide more reasonable control strategies. Tra-ditional TU cooperative games, non-cooperative games,and two-person zero-sum games are special cases of cou-pling game. This paper describes military applications ofcoupling game theory in a Navy research project. Ap-

54 CT07 Abstracts

proaches to determine coupling factors in coupling gamesare discussed. Sensitivity functions of coupling factors areprovided. Experiments confirm the benefits of applyingcoupling game theory to non-ideal complex military situa-tions.

Genshe ChenIntelligent Automation, Inc.Senior Research Scientistgchen@i-a-i.com

MS27

Robust Cooperative Control in Multi-Player Pur-suit Evasion Games with Communication Delays

The performance of the multiple players Pursuit-Evasiongame is often highly dependent on the utilization of thecommunication network. However, it seems like that is-sues of intermittent communications and limited availableinformation have not been adequately addressed. Innova-tive approaches are requested to deal with multiple play-ers PE control issues arising from intermittent and asyn-chronous communications, where pursuer team memberscommunication is limited. To extend our robust cooper-ative control in multiple agent PE game to environmentswith intermittent asynchronous communication, we pro-posed an Open-Loop Asynchronous Feedback Nash Opti-mal (OLAFNO) strategy in this talk. The advantages ofOLFO are 1) OLFO is simple in concept. Open loop op-timization assumes no further feedback beyond the initialidentification and estimates of the system states and pa-rameters; 2) OLFO is an adaptive controller using currentestimates. We also describe a simulation to illustrate theperformance of our proposed approach.

Jose CruzThe Ohio State UniversityDistinguised Professorcruz.22@osu.edu

MS27

Cooperative Control Solutions in Multi-PersonQuadratic Decision Problems: Cost Cumulants andFinite-Horizon Paradigm

In the cooperative control regime using cost cumulants forthe class of multi-person single-objective decision prob-lems characterized by quadratic random costs and state-feedback information structures, individual decision mak-ers share state information with their neighbors and thenautonomously determine decision strategies to achieve thedesired goal of the group which is a minimization of a fi-nite linear combination of the first k cost cumulants of afinite-horizon integral quadratic cost associated with a lin-ear stochastic system, when the decision makers measurethe states. Since this problem formulation is parameterizedby the number of cost cumulants, the scalar coefficients inthe linear combination and the group of decision makers, itmay be viewed both as a generalization of linear-quadraticGaussian control, when the first cost cumulant is mini-mized by a single decision maker and of the problem class oflinear-quadratic identical-goal stochastic games when thefirst cost cumulant is minimized by multiple decision mak-ers. Using a more direct dynamic programming approachto the resultant cost-cumulant initial-cost problem, it isshown that the decision laws associated with multiple per-sons are linear and are found as the unique solutions ofthe set of coupled differential matrix Riccati equations,whose solvability guarantees the existence of the closed-

loop feedback decision laws for the corresponding multi-person single-objective decision problem.

Khanh D. PhamThe Air Force Research LaboratorySpace Vehicles Directoratekhanh.pham@kirtland.af.mil

MS27

Nash and Minimax, Cumulant, Stochastic Differ-ential Games: Going Beyond the Mean

The mean value of a cost plays prominently into controland game theory. Recently cost cumulants have been usedin both control and games. We will extend the use of costcumulants in games to the third and fourth cumulants, forminimax and Nash games. A class of nonlinear systemswith nonquadratic costs are examined. Equilibria for linearquadratic case will be found. This work was supported inpart by Air Force grant number FA9550-07-1-0319.

Ronald Diersing, Chang-Hee WonTemple Universityrdiersin@temple.edu, cwon@temple.edu