Dynamical Networks: Structural Analysis and Synthesis · UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione PhD student: Giulia Giordano

UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it

PhD student: Giulia Giordano Supervisor: Prof. Franco Blanchini

social networks

production anddistribution systems

(bio)chemicalprocesses

A B C

synchronization

telecommunication / data communication networks

water distribution networks

traffic managementbiological systems, ecosystems

DYNAMICAL NETWORKS:structural analysis

and synthesis


Dynamical network:subsystems (each with its own dynamics)interconnected by "flows" / interactions

(hyper-)graph representation:nodes→subsystems

arcs→flows

social networks

production anddistribution systems

(bio)chemicalprocesses

A B C

synchronization

telecommunication / data communication networks

water distribution networks

traffic managementbiological systems, ecosystems

1 2

34

5


1 2

34

5

Compartmental systems...

1 2

34

...generalised

graphrepresentation:nodes→compartmentsarcs→flows

hyper-graph:flows can requireinteractions amongmore than twocompartments

- positive systems- “mass” conservation constraints- flow: interaction between two compartments


A twofold goal

Structural Analysis

...especially meant for...

Structural Control Synthesis

- independent of parameters- based on the nature of interactions (graph topology)- explain robustness and characteristic behaviours

- interactions decided based onlocal information (decentralized)- control / coordinate global system behaviour

Natural Systems Man-made Systems

biologically-inspired design: learn from nature

synthetic biology:engineer natural systems

→ Applications tobiochemical systems

→ Network-decentralized control


Structural Analysis


→Applications to biochemical systems


explain behavioursbased on the system

inherent structure

Biological systems are extremely robust:fundamental properties are preserved

despite huge uncertainties and parameter variations

structure graph

STRUCTURAL ANALYSIS

(...motifs...)

Structural property:satisfied by all the systems of a family

specified by a structure without numerical bounds


stability boundedness

Yes

No

Yes

No

Numerical tests based on polyhedral Lyapunov functionsto structurally assess

F. Blanchini, G. Giordano,“Piecewise-linear Lyapunov functions for structural stability of biochemical networks”, Automatica


Structural graph-based classificationof oscillatory/multistationary behaviours

F. Blanchini, E. Franco, G. Giordano,“A structural classification of candidate oscillators and multistationary systems”, Bull. Math. Biol.

Candidate oscillator

Candidate multistable


Similar results hold for the interconnectionof structurally stable monotone subsystems

F. Blanchini, E. Franco, G. Giordano,“Structural conditions for oscillations and multistationarity in aggregate monotone systems”, submitted

+

+

+

¯

SSMS

SSMS

SSMS SSMS

SSMS

SSMS

Candidate oscillator

Candidate multistable

¯

¯


F. Blanchini, C. Cuba Samaniego, E. Franco, G. Giordano,“Design of a molecular clock with RNA–mediated regulation”, IEEE CDC 2014

x1 z1z3

e2 e1

r2 , e1 , q1

r1 , e2 , q2

z1 , z2 , x3

x1 , x2 , z3

Negative feedback of

two monotone subsystems

Synthesis of biomolecular oscillators


Structural steady-state analysis

Increase Decrease

Perfect adaptation

Depends on parameters

G. Giordano, C. Cuba Samaniego, E. Franco, F. Blanchini,“Computing the Structural Influence Matrix for Biological Systems”, submitted

Input variationOutput variation(at steady state)


G. Giordano, C. Cuba Samaniego, E. Franco, F. Blanchini,“Computing the Structural Influence Matrix for Biological Systems”, submitted

Influence matrix:structural steady-state variation of variable i

due to a persistent additive input applied to variable j

Network fromShinar&Feinberg (2010)

Structural steady-state analysis


Structural Analysis


→Network-decentralized control


huge number of subsystems

subsystemscontrolagents


Control strategy decided locally,to govern the dynamics of the whole system

The feedback matrix has a structure given by the graph

F. Blanchini, E. Franco, G. Giordano, “Structured–LMI Conditions for Stabilizing Network–Decentralized Control”,IEEE CDC13; “Network-Decentralized Control Strategies for Stabilization”, IEEE Trans. Autom. Contr.


Node traffic splitting

Internal node dynamics: stochastic Markov matrix

Network-decentralized control:- robust (independent of Markov coefficients)- optimal: minimum norm (fairness)

F. Blanchini, G. Giordano, P. L. Montessoro,“Network–decentralized robust congestion control with node traffic splitting”, IEEE CDC 2014


PhD results: publicationsJournal papers

* F. Blanchini, E. Franco, G. Giordano, “Network-Decentralized Control Strategies for Stabilization”, IEEE Trans. on Autom. Control, Feb. 2015.* F. Blanchini, G. Giordano, “Piecewise-linear Lyapunov Functions for Structural Stability of Biochemical Networks”, Automatica, Oct. 2014.* F. Blanchini, E. Franco, G. Giordano, “A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems”, Bulletin of Mathematical Biology, Oct. 2014.

Conference papers (peer reviewed)* F. Blanchini, G. Fenu, G. Giordano, F. A. Pellegrino, “Inverse Kinematics by Means of Convex Programming: Some Developments”, IEEE CASE, Gothenburg, August 2015.* F. Blanchini, D. Casagrande, G. Giordano, U. Viaro, “Properties of Switching–Dynamics Race Models”, ECC, Linz, July 2015.* F. Blanchini, G. Giordano, “Structural Stability of Biochemical Networks: Quadratic vs. Polyhedral Lyapunov Functions”, ROCOND, Bratislava, July 2015.* F. Blanchini, G. Giordano, P. L. Montessoro, “Network–Decentralized Robust Congestion Control with Node Traffic Splitting”, IEEE CDC, Los Angeles, December 2014.* F. Blanchini, C. Cuba Samaniego, E. Franco, G. Giordano, “Design of a Molecular Clock with RNA–mediated Regulation”, IEEE CDC, Los Angeles, December 2014.* F. Blanchini, E. Franco, G. Giordano, “Structured-LMI Conditions for Stabilizing Network-Decentralized Control”, IEEE CDC, Firenze, December 2013.


Gantt chartAttività / Mese 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Analisi bibliografia e letteratura

Analisi teorica / Simulaz numeriche

Periodi all'estero

Articoli scientifici e conferenze CD

C

ACC

CDC

Attività formativa scientifica

Corsi formativi complementari

Prep conferenze di dottorato

Preparazione relazioni annuali

Stesura della tesi

Journal/Conference paper

Presentation & Poster

Annual report

PhD thesis

Visits abroad: (1) Supélec, FR, 7-10 April 2014; (2) INP Grenoble, FR, 14-16 May 2014; (3) UC Riverside, CA, USA, December 2014; (4) Universität Stuttgart, DE, March-May 2015.

Papers: (1) Proc. ACC 2013; (2) Proc. CDC 2013; (3) ACS Synthetic Biology; (4) Automatica + Bull Math Biol; (5) Proc. CDC 2014; (6) IEEE Trans Autom Contr; (7) Proc. ROCOND + Proc. ECC 2015.

Training: (1) Photovoltaics: Principles and Devices; (2) Analisi Numerica IV; (3) Metodi topologiciper la ricerca di punti fissi; (4) Scuola Nazionale di Dottorato SIDRA 2013; (5) InterdisciplinaryPhD Spring School; (6) Corso di Deontologia e Pratica Professionale; (7) Lyapunov methodsfor robustness of control systems, PhD School, Grenoble; (8) Il ruolo del ricercatore in Europa;(9) Seminars in Stuttgart; (10) Set theoretic Fault Tolerant Control, Summer School, Grenoble

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Milestones ?

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Researchactivities

Doctoralactivities

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Bibliography and literature review

Analysis /Numerical simulations

Transferable skillstraining

Visits abroad

Papers and conferences

Annual report preparation

Scientific skillstraining

PhD Thesis writing

PhD Conference preparation

Activity / Month

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(7)

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PhD Thesis: Contents (tentative)DYNAMICAL NETWORKS: STRUCTURAL ANALYSIS AND SYNTHESISAbstract1 Introduction2 Structural PropertiesI Background on Dynamical NetworksII Structural Analysis of Dynamical Networks3 Structural Stability and Boundedness4 Structural Classification of Oscillatory and Multistationary Systems5 Structural Steady-State Analysis and Influence Matrix6 How Structural Analysis Can Aid the Synthesis of Biochemical Systems6.1 Design of Biomolecular Oscillators6.2 Rate Regulation in Artificial Gene NetworksIII Structural Control Synthesis for Dynamical Networks7 Network-Decentralized Control Strategies for Stabilization8 Network-Decentralized Congestion Control with Node Traffic Splitting8.1 A Robust Decentralized Control for Channel-Sharing Communication9 Compartmental Flow Control: Decentralization, Robustness and Optimality***10 Conclusions and OutlookIV AppendixBibliography


GRAZIE!

...and still a lot of interesting work to do !

Conclusions

☻

Now there is a PhD thesis to write...

☻

Documents

Dynamical Networks: Structural Analysis and Synthesis · UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione PhD student: Giulia Giordano