Copy of Distributed Collaborative Control for Industrial Automa_new

8/3/2019 Copy of Distributed Collaborative Control for Industrial Automa_new

http://slidepdf.com/reader/full/copy-of-distributed-collaborative-control-for-industrial-automanew 1/11

1

Distributed Collaborative Control for Industrial Automation with

Wireless Sensor and Actuator Networks

Jiming Chen, Member, IEEE, Xianghui Cao, Student Member, IEEE, Peng Cheng, Yang Xiao, Senior

Member, IEEE, and Youxian Sun

Abstract—Wireless sensor and actuator networks (WSANs)bring many benefits to industrial automation systems. When acontrol system is integrated by a WSAN, and particularly if thenetwork scale is large, distributed communication and controlmethods are quite necessary. However, unreliable wireless andmulti-hop communications among sensors and actuators causechallenges in designing such systems. This paper proposes andevaluates a new distributed estimation and collaborative controlscheme for industrial control systems with WSANs. Extensiveresults show that the proposed method effectively achievescontrol objectives and maintains robust against inaccurate systemparameters. We also discuss how to dynamically extend the scaleof a WSAN with only local adjustments of sensors and actuators.

Index Terms—wireless sensor and actuator networks, indus-trial automation, distributed estimation, distributed collaborativecontrol

I. INTRODUCTION

Wireless sensor networks (WSNs) are formed by small-

sized, low cost, and wireless communication capable sensors,

which have been deployed to build various monitoring sys-

tems, e.g., agricultural micro-climate monitoring systems [1].

Wireless sensor and actuator networks (WSANs) introduce

actuators with wireless capability to WSNs to enable wireless

and networked control, actuating, and f eedback [2]. WSANs

have many promising applications in industrial fields, such as

industrial monitoring and control [3], building automation [4],

and manufacturing [5], inventory management [6].

Take the industrial HVAC (Humidity, Ventilation, Air Con-

ditioning) control systems in industrial workplaces as an ex-

ample [7]. We may concern about maintaining the environment

temperatures inside a number of rooms at some comfort levels

(e.g., 20◦C ). We can place some wireless sensors in these

rooms to measure temperatures and report the measurements.

Meanwhile, we may employ some wireless actuators (e.g., air-

conditioners with wireless devices) to heat/cool the rooms.

Manuscript received February 28, 2009; revised July 6, 2009; Accepted

January 5, 2010. This work was supported by National Science FoundationChina-Guangdong Province Union Project under grant U0735003, NationalScience Foundation China under grants 60736021 and 60974122, 863 High-Tech Project No. 2007AA041201 and 111 Projects under grant B07031. Prof.Xiao’s work was partially supported by the US National Science Foundation(NSF) under the grant numbers CCF-0829827, CNS-0716211, and CNS-0737325.

Copyright c 2010 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

J. Chen, X. Cao, P. Cheng and Y. Sun are with the State Key Lab. of Industrial Control Technology, Institute of Industrial Process Control, ZhejiangUniversity, Hangzhou 310027, China. (Corresponding author: J. Chen, email:

[email protected], Tel: +86-571-87953762, Fax: +86-571-87951879).Y. Xiao is with the Department of Computer Science, The University of

Alabama, Tuscaloosa, AL 35487, USA.

Their actuation (e.g., temperature of output wind) is deter-

mined by applying a control law with sensory measurements

as inputs. Integrated with wireless network protocols, real-

time task scheduling strategies [8], and the control law, the

sensors and actuators form a WSAN based on which this

HVAC system can operate both automatically and energy effi-

ciently [9]. Another promising application of WSANs regard-

ing to the industrial lighting systems was presented in [10].

Given the photometric sensors and actuators, e.g., ballasts,

wireless communication capabilities, illumination measuring

(and also control) can be realized for large areas without

massive cabling. The benefits of using WSANs for industrialsystems include ubiquitous information (even in harsh, under-

water, and underground environments), large coverage, fast

communication and reaction, cost saving, easy-installation,

self-organization, and fault tolerance, etc. [11], [12].

Industrial control systems integrated with WSANs have

significant advantages regarding to the ease of sensor and

actuators deployment, network self-organization, and low cost

because of less demands for cables or pre-installed infrastruc-

ture, etc. Their disadvantages, however, can not be ignored

either. In industrial environments, communications within the

WSANs suffer from unpredictable delay, loss, and energy con-

straints. Situation could become even worse when the WSANs

are exposed to environmental interferences such as RF signalsused by other equipments, and also when the WSANs work in

harsh industrial environments, e.g., high-temperature, highly

caustic or corrosive, and dusty environments [6]. Although

delay and packet loss also had been studied widely in the

common networked control systems (NCS), e.g., in [13], [14],

[15], they remain open issues in WSANs. Besides, real-time

and energy efficiency are also important issues [16], [17],

especially when communication links are of low data-rate

(e.g., when IEEE 802.15.4 standard [18] is employed).

Designing wireless and networked control kernel still re-

mains challenging. Control strategies for such systems can be

categorized into following two major kinds, centralized control

and distributed control. For centralized control, system controldecisions are made by a centralized control unit. Examples

include a predictive control for random information delays

[13], a simulated annealing based algorithm for WSANs [19],

signal estimation and control methods in [20], [21] and [22],

etc. For distributed control, no centralized unit is assumed and

control decisions are made by distributed cotrollers/agents or

even by distributed actuators [23], [24]. An outlook of a class

of distributed control is illustrated by Fig. 1, where control

is embedded into the distributed actuators and hence sensors

deliver their measurements of the physical process directly to

the actuators through the wireless media.

Copyright (c) 2011 IEEE

measure andmeasure and controlMeasure and Control for Industrial Automation

using Zigbee and Actuator Networks

Measure and Control for Industrial Automation using

wireless Sensors and Actuator NetworksfdfdfdMeasure and Control for Industrial Automation using

Wireless Sensors and Actuator Networks

copyrights 2010 IEEE

PDFill PD F E

d itor w ith F

ree Writer

and Too ls

http://www.pdfill.com/







































2

Wireless network

SensorsActuators

1

1

1

a

x k C x k

D u k

k E

[ ] [ ]

[ ]

[ ]

Control & actuate

Plant

Sense & report

au x

Fig. 1. Distributed control using wireless sensor and actuator networks.

Industrial automation systems integrated with WSANs re-

quire guaranties for real-timeliness, functional safety, security,

energy efficiency, etc. [25]. These systems can be easily

expanded to large scales due to the easy-deployment and

self-organization nature of the inexpensive sensors and ac-

tuators, resulting in multi-hop fashion of communication if

a centralized control scheme is applied. Consequently, few of

aforementioned guaranties are optimized because of, e.g., high

packet loss and long delay induced by multi-hop transmissions.

To this end, a distributed control scheme can be an alternative

and effective solution which features in f ast reactions to eventsand energy efficiency. Some research challenges of designing

distributed control systems for WSANs are presented in [26].

In the context of wireless networks, a cross-layer design of the

network communications to support distributed control is pre-

sented in [27]. A co-design of network-wide communication

and distributed control methods is presented [28]. However,

distributed estimation and control policies are still challenging

issues which have not been well addressed in the literature.

A distributed control method is designed and compared with

a centralized control method in [29]. It is shown that the

distributed method achieves similar control performances as

the centralized one. However, the designed distributed method

relies on two pre-required parameters, rendering it from beinga wholly distributed and plug-and-run control method.

In this paper, we propose a distributed estimation and

control approach for WSANs1. The contributions of this paper

are stated as follows.

1) A distributed estimation algorithm is proposed which

accounts for not only noisy but also packet loss. We

show that the mean and the variance of estimation errors

are bounded.

2) A distributed collaborative control scheme is presented

based on only local collaborations, which does not

require a specific control phase for the first control step

(as in our conference version [24]).

3) Extensive numerical simulations are conducted to eval-uate the performance of our new methods. The results

show effectiveness of distributed collaborations in the

entire control method, robustness against inaccurate

knowledge of plant parameters, as well as how deploy-

ment of sensors and actuators influences the control

performance.

4) Two mechanisms for dynamically bringing in new sen-

sors and actuators are designed.

The rest of this paper is organized as follows. We model

1The preliminary concept is presented in conference FGCN’08 [24].

the control system in Section II. A distributed estimation

algorithm is proposed in Section III. In Section IV, we design

the distributed collaborative control method. Simulation results

are presented in Section V to show the performance of the

control method. In addition, Section VI discusses the problem

of dynamically extending the scale of WSANs and provides

two useful mechanisms. Finally, Section VII concludes this

paper.

Notations used throughout this paper are defined as follows.

∀θ, θi is its i-th entry if θ is a vector, while θi,j is its (i, j)-th

entry if θ is a matrix. Besides, θT is θ’s transposition. x =[x1, . . . , xns ]T is the system state variable, u = [u1, . . . , una ]T

is the control input to the actuators and ua = [ua1 , . . . , uana ]T

is the vector of actuators output, where ns and na indicate

dimensions. S j and Ai denote the j-th sensor and the i-th

actuator, respectively. Pr{·} and E{·} denote the operators for

probability and estimation, respectively. | · | represents either

the cardinality of a set or the absolute value of a real number.

This can be judged by the context. ∀ variable ϕ, {ϕi} denotes

the set of all possible ‘ϕi’s.

I I . SYSTEM FORMULATION

We consider the WSANs that are employed to NCS for

industrial instrumentation and control applications [3]. Taking

the aforementioned HVAC system for an instance, we view

temperatures inside the rooms as state variables. These vari-

ables need to be maintained to some comfort levels which are

viewed as set-points. The objective is to control the system

state variables to meet the set-points. We focus on a distributed

control mechanism to be embedded into the actuators. In this

section, we present basic models for the system.

We focus on following plant dynamics which is defined in

discrete time domain as below.

x[k] = Cx[k − 1] + Dua[k] + β [k], (1)

where β is a noise of zero-mean. C and D are constant

matrices of appropriate dimensions. We assume that each xj is

measured by a distinct sensor2 S j , where j ∈ {1, · · · , ns}. We

also assume that each uai is actualized by a distinct distributed

actuator Ai where i ∈ {1, · · · , na}. In the aforementioned

HVAC system, x represents the temperatures in these rooms.

Sensors are deployed to measure the temperature, which is

affected by the actuators (e.g., air-conditioners) whose actu-

ation magnitudes (e.g., the output wind temperature) are ua.

The relationship between x and ua is assumed to be a linear

time-invariant (LTI) equation as shown by Eq. (1). By Eq. (1),we assume that the current temperatures inside those rooms

linearly relate to those temperatures in previous time instance

and the actuators output.

Given above plant model, the relations between the sensors

and actuators can be described by two graphs:

1) The graph for physical process, G p (V p, E p). G p is a

directed graph, where the set of vertexes is V p = {Ai} ∪{S j},

2In industrial applications, a state variable may be measured by a sub-network of sensors which adopt certain data aggregation methods to providethe control unit(s) with more reliable data. For simplicity, we, instead, use asingle sensor to model the gross effect of the sensors in that sub-network.

Fig.1 Control using Wireless Networks

wireless technology plays an effective role in the field of autom

-ation and they are the boom for the future .

PDFill PD F E

d itor w ith F

ree Writer

and Too ls








































































3

and the set of edges is E p. ∀ν ∈ V p, let the corresponding

variable of ν be xj (if ν ∈ {S j}) or uai (if ν ∈ {Ai}). ν has

an edge to ν (ν ∈ V p), i.e., ∃E p(ν, ν ), if the corresponding

variable of ν is influenced by (as can be judged by Eq. (1) or

Eq. (4)) the corresponding variable of ν . Define the following

two sets: the influenced sensors of Ai, ∀i ∈ {1, · · · , na},

S Ai = {S j |S j ∈ V p, ∃E p(Ai, S j)} = {S j |dj,i = 0}, (2)

and the responsible actuators of S j , ∀ j ∈ {1, · · · , ns},

ASj = {Ai|Ai ∈ V p, ∃E p(Ai, S j)} = {Ai|dj,i = 0}. (3)

We assume that the dynamics of xj is not inter-connected with

others, i.e., cj,l = 0 if j = l. This means that the edges of G p

are all from actuators to sensors and sensors to themselves.

xj [k] = cj,jxj [k − 1] +

Ai∈ASj

dj,iuai [k] + β j [k]

+

1≤l≤ns;l=j

cj,lxl[k − 1] +

Ai /∈ASj

dj,iuai [k]

= cj,jxj [k − 1] + Ai∈A

Sjdj,iu

a

i [k] + β j [k]. (4)

2) The graph for networked communications, Gc

(V c, E c), which is an undirected graph, where V c = V p. ν

and ν has an edge (ν, ν ∈ V c), i.e., ∃E c(ν, ν ), if they

are connected by wireless links. We assume that the network

is such connected that each sensor has a path to any of its

responsible actuators, and vice versa.

The measured value of xj [k] by sensor S j is assumed to be

yj [k] = xj [k] + γ j [k], (5)

where γ j denotes the measurement noise. Assume that γ j is

white Gaussian and has zero-mean. From Eq. (4), the effectsof all actuators belonging to ASj will overlap at xj . I t is

interesting to define an overlapping degr ee at xj as

ρj |ASj |, j = 1, . . . , ns. (6)

In the k-th step (k ≥ 1), Ai applies certain control law and

decides its control input to be ui[k], which adjusts Ai’s output

from uai [k − 1] to uai [k].

uai [k] = uai [k − 1] + ui[k] + αi[k] (7)

where αi is noise which models the derivation of the real

output from that as expected by Ai. αi is also assumed to

be of zero-mean. We assume that each u

a

i [k] is known byAi. Otherwise, a simple Kalman filter [30] can be used by

Ai to estimate uai [k] according to Eq. (7) and a feedback

measurement of uai [k].Consider the control objective as to meet the set-point p =

[ p1, . . . , pL]T . The control objective can be thus defined as

min : f [k] 1

ns

nsi=1

( pi − xi[k])2. (8)

In the following, we propose a distributed collaborative control

method which comprises of distributed estimation, optimal

control and local collaboration, as shown in Fig. 2.

estimation

optimal control output

iY

i

iuc

a

iu

i P

actuator i

A

collaboration{ }

ijv

iu

Plant

W i r e l e s s n e t w o r k

other actuators

Fig. 2. Components of an actuator for distributed and collaborative control.

III. DISTRIBUTED ESTIMATION

In this section, we present a distributed estimation algorithm

for estimating {xj} that is operated by each of the actuators.

For a single actuator, its control decision relies on the local

information that it can receive from its influenced sensors.

Such information is noisy and intermittent because of sensory

measurement noises (Eq. (5)), packet loss and delay, for which

a method for the actuators to perform estimation of required

information is quite necessary. In [31], Kalman filtering basedestimation over a lossy wireless channel is analyzed and the

bounds of packet loss rate for estimation convergency are

obtained. It is difficult to extend this work to distributed

estimation since it focuses on only a single link between a

sensor and an estimator. Distributed estimation methods for

use with wireless and distributed networks are studied in

[32], [33]. A consensus based distributed estimation approach

(sometimes integrated with Kalman filter) is commonly used,

in which every sensor performs estimation based on only

neighboring sensors’ information. However, these estimation

processes run with a sensor network in which sensors observe

and measure a same physical process state. In this paper, the

estimation problem is different for two reasons: 1) the sensorsare used to measure a group of physical variables, i.e., {xj}; 2)

estimation is performed by each of the actuators with process

state observations sent from the sensors.

In the following, we do not assume packet delay and only

focus packet loss. Packet delay can be treated by augmenting

the system dimensions, e.g., [34]. Moreover, given the discrete

step period, we can count the packets whose delay is large

enough (such that they do not reach their destinations within

the current step) as packet losses. In this case, the estimation

under packet delay can be studied similarly as packet loss.

∀i ∈ {1, . . . , na}, let

Y i[k] = {yj [k]|S j ∈ S Ai and yj [k] is

correctly received3 by Ai}. At the k-th step,

x(i)j [k] E{xj [k]|Y i[k]; Ai}, (9)

which means that x(i)j [k] is the estimate of xj [k] in the

view of Ai. We model the wireless channel between the

sensors and actuators via the following erasure model [35].

∀ j ∈ {1, . . . , ns}, ∀i that Ai ∈ ASj and ∀k > 0, define a

Bernoulli random variable ωji[k] (Pr{ωji[k] = 1} = ωji) to

describe the packet transmission successfulness from S j to Ai

as below.

3In terms of “correctly receive”, we mean that the packet, e.g., the packetof yj [k], is received by Ai before it starts to estimate in the k-th step.

components with actuator network

PDFill PD F E

d itor w ith F

ree Writer

and Too ls


















































































4

1) If yj [k] is correctly received by Ai, ωji[k] = 1. Our

estimation algorithm in this case is such that x(i)j [k] is

a linear combination of the previous step estimate and

the current step sensor measurement, i.e.,

x(i)j [k] = q[k]x

(i)j [k − 1] + (1 − q[k])yj [k]. (10)

2) Otherwise, ωji[k] = 0. In this case, The estimation could

only rely on its historical estimates. Whereas, if weonly use the historical data, in the case that packets are

continuously lost, the estimate will become too old and

even meaningless. Instead, we introduce the set-point

pj to the estimation algorithm (Eq. (12)) based on an

assumption that x[k] approaches p step by step with the

efforts of the actuators, so that xj [k] will get close to

pj after a number of steps, say K , of control, i.e.,

|xj [k] − pj| ≤ ∆, when k > K. (11)

x(i)j [k] = t[k]x

(i)j [k − 1] + (1 − t[k]) pj. (12)

We will use constant q and t instead of q[k] and t[k] in

the following. Define the estimation error e(i)j [k] = x(i)j [k] −xj [k]. The following propositions are useful for evaluating the

estimation performance.

Proposition 1: If |q| < 1, |t| < 1 and Eq. (11) holds, then,

limk→+∞

|E{e(i)j [k]}| ≤

|ωji(q − t) + t|

1 − |ωji(q − t) + t|Ξji, (13)

where

Ξji =

1 +

ωji − ωjiq − 1

ωji(q − t) + t

∆ + | pj |

+

(1 − ωji)(1 − t)

ωji(q − t) + t

·| pj |. (14)

Proof: Our estimation algorithm described by Eq. (10)

and Eq. (12) can be summarized by

x(i)j [k] = ωji[k]

qx

(i)j [k − 1] + (1 − q)yj [k]

+ (1 − ωji[k])

tx

(i)j [k − 1] + (1 − t) pj

. (15)

Thus the estimation error is

e(i)j [k] = (ωji[k]q + t − ωji[k]t)e

(i)j [k − 1]

+ (ωji[k]q + t − ωji[k]t)xj [k − 1]

+ (ωji[k] − ωji[k]q − 1)xj [k]

+ ωji[k](1 − q)γ j [k] + (1 − ωji[k])(1 − t) pj . (16)

Consequently,

|E{e(i)j [k]}| ≤ |ωji(q − t) + t|

|E{e

(i)j [k − 1]}| + Ξji

≤ Ξji

|ωji(q − t) + t| − |ωji(q − t) + t|k+1

1 − |ωji(q − t) + t|

+ |ωji(q − t) + t|k · |E{e(i)j [0]}|, (17)

where Eq. (11) and that γ j [k] has zero-mean are used in above

deduction. One can easily see that 0 ≤ ωji ≤ 1, hence |ωji(q−t) + t| ≤ max{|q|, |t|} < 1. Eq. (13) can be then proved by

taking the limit of above equation for k → +∞.

Proposition 2: If the conditions in Proposition 1 are all

satisfied, then,

limk→+∞

E

e(i)j [k]

2≤

|ωji(q2 − t2) + t2|

1 − |ωji(q2 − t2) + t2|Ξji, (18)

where Ξji is a regular function of ∆, | pj |, ωji, q , t and

E{γ 2j [k]}.

This can be proved in the very similar way as that for

Proposition 1.

Remark 1: Above two propositions suggest that if q and

t are determined, we could make the mean and variance of

the estimation error bounded, i.e., |E{e(i)j [k]}| < ∞ and

E

e(i)j [k]

2< ∞. However, that this fact does not guarantee

an unbiased estimation imposes a strict constraint on choosing

t so that the control performance will not get divergent.

Besides, the selection of t apparently relates to packet loss.

Section V will choose q = 0.1 and t = 0.9 for the simulation

settings. It is shown that the optimal t is around 1 when there’s

no packet loss. This optimal t moves towards 0 when the

packet loss rate grows.

IV. DISTRIBUTED COLLABORATIVE CONTROL

At this stage, each actuator uses the estimated local state

variables to decide its control input. We first let Ai calculate

its optimal control input ui without collaborations with others,

and then use ui as a bid for negotiating with other actuators.

A. Optimal Control Without Collaborations

The output of Ai, i.e., xi, influences the variables hat are

measured by the sensors in S Ai . Similarly to ρj , We define

µi = |S Ai |, i = 1, . . . , na. (19)

Apparently, if µi = 1, the variable xj (S j = S Ai ) will be

fully controlled by Ai. Let’s define a sequence { j1, . . . , jH }where j1 < . . . < jH , j1 ∈ {1, . . . , ns}, H = µi and

S jh ∈ S Ai (1 ≤ h ≤ H ). Define X i = [xj1 , . . . , xjH ]T ,Di = [dj1,i, . . . , djH ,i]

T , Bi = [β j1 , . . . , β jH ]T and P i =[ pj1 , . . . , pjH ]T . From Eq. (1), we can deduce that

X i[k] = C iX i[k − 1] + Diuai [k] + Γi[k] + Bi[k], (20)

where C i is a diagonal matrix whose (h, h)-th entry is cjh,jh(S jh ∈ S Ai , 1 ≤ h ≤ µi). Γi accounts for the effects of the

actuators on X i other than Ai. From Eq. (4), ∀h(S h ∈ S Ai ),

the h-th element of Γi[k − 1] is

Γi,h[k] = Al∈A

Sh ; l=i

dh,lual [k]. (21)

The term Γi[k] is unknown for Ai which decides its control

input ui[k] in a distributed way.

∀i ∈ {1, . . . , na}, the only part of the control objective on

which Ai has an effect is

f i[k] 1

ns

Sj∈SAi

( pj − xj [k])2

=1

ns(P i − X i[k])T (P i − X i[k]). (22)

PDFill PD F E

d itor w ith F

ree Writer

and Too ls















































5

The following theorem gives us the optimal control input

of Ai to minimize f i[k] before collaboration.

Theorem 1: After k − 1 steps and before making k-th

decision, Ai’s optimal control input ui[k] that minimizes f i[k]when firstly without collaborations with other actuators is

ui[k] =1

DT i Di

DT i

P i − C iX i[k]

−uai [k − 1], (23)

where the j-th element of X i[k] is x(i)j [k], 1 ≤ j ≤ µi.

Proof: From Eq. (7), Eq. (20) and Eq. (22), we have

f i[k + 1] =1

ns(Diui[k] − Qi[k])T (Diui[k] − Qi[k]), (24)

where Qi[k] = P i − C iX i[k] − Diuai [k − 1] − Γi[k] − Bi[k] −

Diαi[k]. Then

E{f i[k + 1]} =1

ns

DT i Diu

2i [k] − 2DT

i E

Qi[k]

ui[k]

+ E

QT i [k]Qi[k]

=1

ns

E

QT i [k]Qi[k]

−2DT

i

P i − C iX i[k]

− Diuai [k − 1]

ui[k] + DT

i Diu2i [k]

, (25)

where we used the assumptions that the noises are of zero-

means. Because Ai does not exchange information with other

actuators at this stage, Γi[k] is unknown to Ai and we use

E{Γi[k]} = 0.

∂ E{f i[k + 1]}

∂ui[k]=

1

ns

DT i Diui[k] − 2DT

i

P i − C iX i[k]

− Diua

i [k − 1] (26)

By letting above equation to be 0, we can obtain the optimal

solution of ui[k] as stated in Theorem 1.

B. Local Collaborations and Control

If each actuator uses Eq. (23) as its final control inputs

and then adjusts its actuation, the whole system will probably

becomes unstable because of overlapping actuation, i.e., the

actuation will be doubled or even multiplied at the variables

where the overlapping degrees are larger than 1. To show this,

let us consider the following simple example. Suppose that two

actuators, say A1 and A2, influence a common state variablex and a sensor S 1 is placed to sense x, i.e., S A1 = S A2 = S 1,

AS1 = {A1, A2}, and ρ1 = 2. Apparently, if both actuators

try to move x from its initial state x0 to set-point p without

caring the actuation of each other, their actuation will always

be doubled at S 1. Thus, x will become shifting between x0

and 2 p − x0, and never converge to p unless p = x0.

To this end, each actuator Ai collaborates with its neighbor

actuators in the purpose of compensating the overlapping

actuation. In terms of “neighbor actuators” (denoted by N i),

we mean the actuators with which Ai needs to exchange in-

formation. From Eq. (21), we can understand that N i contains

the actuators which and Ai share at least one same influenced

sensor, i.e.,

N i =

Al|∃ j,S j ∈ S Ai , Al ∈ ASj

(27)

By exchanging information with all Al ∈ N i, Ai is able to

have a better knowledge of Γi, and thus have more information

about the local states dynamics as in Eq. (20).

In order to depress the overshooting caused by overlapped

actuation, we introduce for Ai a tunable factor λi[k] < 1 to

the optimal control input ui[k], such that

ui[k] λi[k]ui[k]. (28)

λi[k] is called the tuning parameter. If S j’s responsible ac-

tuators contain both Ai and Al, by Eq. (21), their ultimate

effects will overlap at xj if dj,ixi and djlxl have the same

sign (positive and negative). This leads to overshoot of their

actuation at xj . With this observation in mind, we design the

distributed collaboration mechanism as follows.

actuator

sensor

2S

3S

4S

1uc

3uc

2uc

11v

31v

21v

A

A

A

1 A

2 A

3 A

1S

Fig. 3. An example illustrating the procedure of distributed collaborativecontrol. It also shows the Gp, in which an actuator has an edge to a sensor if the latter is inside the circular range of the former. The circles are just usedfor illustration.

For the sake of clearly describing the way of obtaining λi[k],we uses the following example to illustrate the process. Let’s

take the G p shown in Fig. 3 and the process to define λ1[k]for A1 as an example.

1) Prediction. Firstly, A1 predicts its output by ua

1[k] ua1[k − 1] + u1[k] and the ultimate effect set

{dj1ua

1[k], j = 1, 2, 3, 4}, where u1[k] is calculated by

Eq. (23) based on only local information.

2) Exchanging local information. A1 then sends the in-

formation of ultimate effect set to all the sensors inS A1 . Similarly do the other actuators. When S 1 receives

this information from A1, A2 and A3, it gets the set

{d1iua

i[k], i = 1, 2, 3}. It then counts the numbers of

elements in that set that have the same sign as one

another, and thus gets the numbers {vi1[k], i = 1, 2, 3}.

vi1[k] means the number sent by S 1 to Ai at the k-th

step. Heuristically, Ai should reduce u1[k] by a factor1

1+v11[k]in order to compensate the overshooting if no

packet loss takes place.

3) Dealing with packet losses. If, for example, the packet

of d13ua

3[k] gets lost, S 1 will count it as of the same

5

PDFill PD F E

d itor w ith F

ree Writer

and Too ls




































6

sign as u1[k]. Then S 1 informs each Ai (i = 1, 2, 3)

of vi1[k]. If, for example, the packet of v13[k] is not

correctly received by A3, A3 will let v13[k] = ρ3 − 1.

4) Obtaining the tuning parameter . After obtaining all

v1j [k] (S j ∈ S A1), A1 will define its overshooting

depressing factor by averaging the factors { 11+v1j [k]

},

i.e.,

λ1[k] 1µ1

Sj∈SA1

11 + v1j [k] , k > 1 (29)

In the same way, each actuator can calculate its own λi[k] via

indirect communications with neighbors. In terms of “indirect”

we mean that the information exchanging among between each

actuator and its neighbor actuators is actually carried out by

the sensors.

Remark 2: Recall that ρj is the overlapping degree at S j .

The larger ρj is, the more information the actuators in ASj

should exchange with each other, and thus the more complex

for the actuators to collaborate with each other. Let ρ and µ be

the average values of {ρj} and {µi}, respectively. Observing

that µna = ρns, µ can also be viewed as an indicator of thecollaboration complexity. We will see in the next section how

µ effects the control performance.

Remark 3: If |cj,j| < 1, ∀ j ∈ {1, . . . , ns} and the

actuation ua[k] is bounded, from Eq. (1), one can easily see

that the state x[k] is always bounded. The method discussed

above is a heuristical method and it is hard to give an analytical

description of the control performance, however, we will show

the system stability and the method’s effectiveness in achieving

the control objective by extensive numerical simulations in the

next section.

V. NUMERICAL EXAMPLES

A. A Simple Example

First, we consider a very simple HVAC system for tem-

perature control with two sensors and two actuators, i.e.,

ns = 2, na = 2. We aim at best meeting the set-points

( p = [16(◦C ) 18(◦C )]) at the two sensor places. The plant

model parameters (see Eq. (1)) are

C =

0.9 00 0.9

, D =

0.57 00.49 0.68

. (30)

In the simulations, we apply an actuation bound to the ac-

tuators such that uai ∈ [−5 5]. We are going to show the

overshooting phenomena caused by the distributed optimal

control without local collaborations. The simulation results of the actuators performances u1[k] and u2[k], are shown in Fig.

4. From Fig. 4(a), we observe that, without collaborations,

the actuators outputs vary violently and thus cause actuation

overshooting. Comparing Fig. 4(a) with Fig. 4(b), we can see

that the local collaborations among the actuators mitigate the

violent actuation significantly and also u1[k] and u2[k] both

converge to their stable states.

B. A More General Example

In the next, we consider another similar but more compli-

cated example in which ns = 48 and na = 24. We use 48

0 100 200 300 400 500-15

-10

-5

0

5

10

15

k

u2[k]

u1[k]

(a) without local collaborations.

0 100 200 300 400 500-15

-10

-5

0

5

10

15

k

u2[k]

u1[k]

(b) with local collaborations.

Fig. 4. The effect of local collaborations.

sensors to measure the temperature at each of the sensor place,

i.e., xj , and a group of 24 actuators to carry out each of the

ui. The average of {µi} is µ = 12, i.e., the average number

of influenced sensors for each actuator is 12. The plant model

parameters are set as follows. cj,j = 0.9, ∀ j ∈ {1, · · · , ns}.dj,i is randomly chosen from (0, 1] if S j is one of Ai’s

influenced sensors. The set-points, { pj}, are randomly chosen

from [0(◦C ), 30(◦C )]. For distributed estimations, we use the

following parameters: q = 0.1, t = 0.9. The system noises

α, β and γ are set to be Gaussian white noises with zero

means. In this simulation, we assume that the devices know

exactly the values of the terms {dj,i} whenever required.

Simulation results when the DCC method is applied are shown

in Fig. 5. The optimal f [k] 4 is calculated by the centralized

control method as presented in [29] in the ideal case (i.e.,

without system noises, packet loss or any bounds on the

actuation ua[k] and system state x[k]). It is the optimum value

of f [k] the whole control system could be able to achieve. In

Fig. 5(a), the results illustrate the (optimal) performance of the

DCC without uncertain terms (i.e., there is no system noises

and the packet loss rates are 0). In this case, we can easily

see that the system is stable. In practical cases (i.e., with the

uncertain terms), Fig. 5(b) plots the evolutions of f [k] under

several system noise levels. In the simulations, all the systems

4The optimal f [k] is obtained in the following way. Recalling Theorem1, let Ai be the centralized controller that knows the whole plant model.Substituting corresponding global terms for the local terms (e.g., p for P i),we obtain the optimal control input for all the actuators. Applying this inputto the plant we can get the optimal f [k].

fig b range of temperature value with the set

point

PDFill PD F E

d itor w ith F

ree Writer

and Too ls

















7

noise sequences, i.e., {αi[k]}, {β j [k]} and {γ j [k]}, are set to

have the same noise power. The average packet loss rates for

the communication between sensors and actuators are set to be

20%, i.e., the average packet reception rate is ω = 80%. It can

be seen that, when P noise is low, f [k] becomes approximately

stable such that it starts to vary within a very small range after

a number of steps. When P noise grows, the varying range of

f [k] increases.

0 20 40 60 80 1000

20

40

60

80

100

k

f [ k ] ( % )

optimal f[k]

optimal performance of DCC

(a) Without the uncertain terms.

0 100 200 300 400 5000

20

40

60

80

100

k

f [ k ] ( % )

optimal f[k]

Pnoise

= 2

Pnoise

= 1

Pnoise

= 0.1

(b) With the uncertain terms.

Fig. 5. Performance of the DCC. P noise is the power of the system noises.

In the following, we further evaluate the effects of the

system parameters on the performances of the proposed es-

timation and control methods. We introduce the following

term as the estimation performance metric: σe, which is the

mean of all the square estimation errors, i.e., all {(e(i)j [k])2}.

The smaller σe is, the better the estimation method performs.

In practice, to evaluate the simulation results, what we may

care about are: the final stable f [k] the system achieves, andthe converging speed of f [k]. To consider the converging

speed, we give a tolerant period, which is set to be the

period of the first 100 steps, for f [k] to converge, and use the

statistics after 100-th step to calculate the following metrics:

f m, which averages f [k], and σf , which is the variance of f [k].Obviously, a small f m indicates, averagely, that the system

achieves a small final value of the objective function and thus

the final differences between the system states and the set-

points are small. σf suggests whether the system varies too

much. Besides, if f [k] cannot converge before that tolerant

period, σf will report a large value.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

30

60

90

120

150

180

q

Ve

(t = 0.9)

f m

(t = 0.9)

Vf (t = 0.9)

Fig. 6. Control performances with respect to various q.

C. Optimal Estimation Parameters: q and t

The parameter q (see Eq. (10)) is the weight of the historical

data in the current estimate. When we fix t at 0.9, the

performances of the DCC with respect to various values of

q are shown in Fig. 6. It is suggested by this figure that the

acceptable range of q is in [0, 0.4]. When q is too large, thehistorical estimate will dominant the current estimate such that

the sensory measurements cannot update the estimate in time.

Otherwise, when q is too small, the measurement noises will

become to disturb the estimate. The parameter t is responsible

for the cases of pack et loss. From Fig. 7, we can see that at a

given packet loss rate, the effect of introducing the set-point

into the estimation algorithm is evident since the estimation

and control when 0 ≤ t < 1 outperform those when t = 1.

We also see that the optimal t is related to the average packet

reception ratio ω when q is fixed. As ω increases, the optimal

t also increases until 1 if we also choose σf as the criteria.

D. Impact of Packet Loss

Observed from the proposed distributed estimation and

control processes, packet loss harms not only the estimation,

but also the control performance. Seen from Fig. 7, increasing

the packet loss rate (or decreasing the packet reception rate)

will cause: (1) increase of the estimation bias; (2) increase of

the variance of the estimation error; (3) degrading the objective

function the system could achieve, and (4) increase of the

variance of the objective function estimation error.

E. Robustness Against Inaccurate Knowledge of {dj,i}

In applications that exact {dj,i} could not be obtained, the

system robustness against inaccurate knowledge of {dj,i} isan important metric of the system performances. Simulation

results are illustrated in Fig. 8. We let the knowledge of

corresponding sensors/actuators about the coefficient dj,i to be

the combination of the real dj,i and an additive white gaussian

noise, which ranges from 0% to 30% percent. From Fig. 8(a),

we observe that when the additive noise percents are smaller

than 20%, the objective function evolution curves are very

close to that when the knowledge is accurate. In Fig. 8(b),

it is shown that increasing the percent of the additive noise

does not make significant changes to the whole performances

especially when this percent is less than 20%.

PDFill PD F E

d itor w ith F

ree Writer

and Too ls

































8

0 0.2 0.4 0.6 0.8 1

0

30

60

90

120

t

V e

Z = 20%

Z = 40%

Z = 60%

Z = 80%

Z = 100%

(a)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

t

f m

Z = 20%

Z = 40%

Z = 60%

Z = 80%

Z = 100%

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

t

V f

Z = 20%

Z = 40%

Z = 60%

Z = 80%

Z = 100%

(c)

Fig. 7. Control performances with respect to various t and packet receptionrates.

F. Effect of µ

The average number of influenced sensors of the actuators

represents the complexity for actuators to collaborate witheach other. When µ increases, the complexity grows up. On

one hand, Fig. 9 suggests that a high µ is unadvisable since the

collaboration process will become complicated. The extreme

case is that µ = ns such that the control decision process for

each distributed actuator will become as complicated as that

for a centralized controller. On the other hand, a small µ may

also be inadvisable since some of sensors may become the

influencing sensor of none of the actuators. Above all, good

control performances may require that µ is neither too small to

avoid uncovered sensors by the actuators influencing ranges,

nor too large to avoid high collaboration complexity.

0 100 200 300 400 5000

20

40

60

80

100

k

f [ k ] ( % )

0%

5%

10%

20%

30%

(a) Performances under different additive noise percents.

0 5 10 20 300

2

4

6

8

percent of additive noise (%)

Ve

f m

Vf

(b) Performance comparison in terms of σe, f m and σf .

Fig. 8. Performances when the knowledge of the coefficients {dj,i} isinaccurate.

0 100 200 300 400 5000

20

40

60

80

100

k

f [ k ] ( % )

P = 5

P = 20

P = 35

(a) Performances under different µ.

5 10 15 20 25 30 350

2

4

6

8

10

12

P

Ve

f m

Vf

(b) Performance comparison in terms of σe, f m and σf .

Fig. 9. Performances regarding to average number of influenced sensors of the actuators.

PDFill PD F E

d itor w ith F

ree Writer

and Too ls







9

V I . EXTENSION TO LARGE SCALE

So far we have been considering the WSANs with fixed

number of sensors and actuators (or simply fixed scale). In in-

dustrial applications, WSANs are required to cover a large area

of interests by dense sensing and effective actuation. In other

words, large-scale WSANs are demanded [6]. Although, we

can conclude from above presentations that our distributed col-

laborative control method is valid for WSANs of any scale, weare hereafter concerned with dynamically extending the scale

of a current running WSAN. There are many practical reasons

why such a dynamic extension is necessary, e.g., incorporating

another workplace or physical process to the current one

which is monitored and controlled by a WSAN; introducing

new actuators to augment the collective actuation capability

of current WSAN; replacing depleted sensors/actuators with

fresh ones5. In [29], the distributed control method based

on artificial neural network shows similar performance as

the centralized control method, in terms of reducing system

residual error, while it is more energy economic. However,

the two critical parameters η and λ should be defined before

running the control system. The change of network topologywill potentially deteriorate the whole system performance.

Therefore, the whole system should reanalyze itself and adjust

the above parameters for each actuator in a centralized way.

When the distributed collaborative control method is applied,

there is no predefined global parameters for the whole system

to run with. To this end, the scale of the WSAN can be

extended without constraints.

In this section, we first assess the difficulty of extending the

WSAN with our proposed method applied. Then we present

two mechanisms for the network to extend its number of

sensors or actuators, respectively.

A. Extensibility

By extensibility, we mean the cost of extending the network

scale in terms of control complexity, the increased communi-

cation overhead, and the difficulty of adding sensors/actuators.

In the following, the extensibility of WSAN with distributed

collaborative control (DCC) as presented in this paper will be

compared with that of WSAN with centralized control (CC)6

as presented in [29].

1) Control Complexity: The control complexity can be

interpreted as the following two terms.

First, we consider the computational complexity of the

control algorithm. Higher complexity requires richer compu-tational resources, so that excessive network scale is discour-

aged. It can be proved that the complexity of CC is in the

order of O(n3s)+O(n3

a) because of the quadratic programming

method [29]. In the DCC, from Eq. (23) and Eq. (29), the

control complexity for Ai is O(µi). Therefore, compared

with DCC, the control complexity of CC grows much more

dramatically along with the increasing the numbers of sensors

or actuators.

5The case is similar as that of adding new sensors/actuators if we focus ondesigning the mechanisms for the newly introduced devices.

6It is representative of commonly used centralized control methods.

Second, we consider the amount of necessary information

from corresponding sensors/actuators to make the control de-

cision. The more necessary information the control algorithm

needs, the more quickly its one-hop neighbors are consumed

up and thus the whole control system fails to function. In

the CC, the necessary amount of information, in terms of

number of packets, for the centralized controller is nCC =(ns + na) in each step. In the DCC, this amount for Ai is

nDCC = (µi +Sj∈SAi

ρj) (see the calculations of Eq. (23)

and Eq. (29)) in a single step. If we assume that the sensors and

actuators are uniformly deployed inside a circle of radius R

with densities ξs and ξa respectively, and that the influencing

range of every actuator is r, we have ξs = nsπR2 and ξa = na

πR2 .

Hence the average nDCC (taken over all actuators) becomes

nDCC =r2

R2ns +

r2

R2ns

r2

R2na =

r2

R2ns

1 +r2

R2na

= πξsr2(1 + πξar2). (31)

The above equation reveals that the increase of sen-

sors/actuators without changing the deployment density will

increase the complexity of the CC but not that of the DCC.2) Extending Difficulty: One way to measure the difficulty

is by measuring the number of devices that need updating

caused by the introduction of new sensors/actuators. In the CC,

the centralized controller should update its control parameters

in order to accommodate those new sensors/actuators in the

control algorithm. Except for routing updating, the increase

of devices leads to only the controller updating. In the DCC,

newly introduced sensors/actuators will cause updating of mul-

tiple sensors/actuators functionalities. Taking the introduction

of a new actuator as an example, it will cause its influenced

sensors and neighbor actuators update their functionalities.

Therefore, the average number of devices need updating is

the same as nDCC in Eq. (31), which is bounded.From above discussions, the DCC has much lower con-

trol complexity but higher extending difficulty than the CC.

However, that extending difficulty of the DCC is bounded.

Hereafter, we design two mechanisms for adding a single

sensor (or actuator) as presented as follows. We assume that

each device knows its spatial position.

2S

3S

4S

1S 5S

A

A

A

A

actuator

sensor

1 A

2 A

3 A4

2( ) Apply S

1 2( , )reply A S

Fig. 10. Adding an actuator A3 and a sensor S 2 to the network.

7

PDFill PD F E

d itor w ith F

ree Writer

and Too ls
















































10

B. Adding a Sensor

When a new sensor node is introduced to a well designed

WSAN, according to our distributed collaborative control

method, it should find out its responsible actuators and an-

nounce them of its participation. Take the example shown

in Fig. 10, and suppose that S 2 is a new sensor node. It

first broadcasts application packet Apply(S 2) to the network,

where Apply(S 2) contains the information of a symbol of application packet and the ID and location of S 2 itself.

On receiving Apply(S 2), an actuator, e.g., A1, first checks

whether S 2 is inside its influencing range (i.e., whether the

variable defined at S 2 is influenced by A1) by calculating the

distance between them. If S 2 is inside that range, A1 will enlist

S 2 into its set S A1 and reply S 2 by a packet Reply(A1, S 2). If

not, A1 just ignores Apply(S 2). When Apply(S 2) is relayed

by other sensors to all actuators in AS2 , upon reception of

Apply(S 2), an intermediate sensor will forward Apply(S 2)only if S 2 falls inside the influencing range of any of its

responsible actuators. In this way, the spreading of Apply(S 2)is bounded and thus S 2 only cause local adjustments of the

other sensors and actuators. On receiving Reply(A1, S 2), S 2will enlist A1 into its set AS2 . In this way, the responsible

actuators are known by S 2, and S 2 is enlisted into the

influenced sensors of each of those actuators. At this time, S 2needs to communicate with each of its responsible actuators

in order to calculate the term dji as in Eq. (4). In the following

control steps, each of actuators belonging to AS2 sends their

output xi[k] to S 2 during the collaboration stages (see Section

IV-B). By examining the relationship between m2[k] and xi[k](Ai ∈ AS2) for no less than ρ2 control steps, S 2 is able

to estimate all d2i according to Eq. (4). The noises β and

γ are not accounted in above estimations, so above process

should be carried for more steps for S 2 to get a more accurate

estimations of d2i (Ai ∈ AS2). Note that it is shown in SectionV that our distributed collaborative control is robust against

the inaccurate knowledge of the terms dji. Therefore, above

inaccurate estimations of d2i are tolerable.

C. Adding an Actuator

Additional actuators may need to be introduced to the

system when present actuators are inadequate to achieve the

control objective. A new actuator should communicate with

other sensors to discover its influenced sensors and estimate

the corresponding terms of dji . Take the example shown in

Fig. 10 where A3 needs to join the network. It first broadcasts

an application packet over the network. On receiving this

packet, a sensor will check if it is in A3’s influencing range. If

so, it replies A3. Then A3 is able to find out its set S A3 . It uses

a random value as its output, and informs each of its influenced

sensors of x3[k] during the collaboration stage. Unlike adding

a sensor, the sensor S j (S j ∈ S A3) can estimated dj3 in each

step by examining the relationship between mj [k] and x3[k].The estimated value of dj3 will be sent to A3 for next step’s

control decision.

VII. CONCLUSION

In this paper, a distributed collaborative control (DCC)

method is proposed for industrial control applications with

WSANs. In order to cope with sensory measurement noises

and packet loss in wireless communications, a distributed

estimation is designed, based on which a locally collaborative

control algorithm is presented, which fully exploits the col-

laborations between actuators and sensors. The effectiveness

is shown by extensive simulation results. We also show how

the results could accommodate the case where sensors and

actuators could be introduced dynamically.

ACKNOWLEDGEMENT

The authors would like to thank the Associate Editor and

anonymous reviewers for their valuable comments which help

us improve the quality of the manuscript.

REFERENCES

[1] X. Cao, J. Chen, Y. Zhang, and Y. Sun Development of an integratedwireless sensor network micro-environmental monitoring system. ISATransactions, 47(3):247–255, Jul. 2008.

[2] I.F. Akyildiz and I.H. Kasimoglu. Wireless sensor and actor networks:research challenges. Ad Hoc Networks (Elsevier), 2(4):351–367, 2004.

[3] H. Ramamurthy, B.S. Prabhu, and R. Gadh. Wireless industrial moni-toring and control using a smart sensor platform. IEEE Sensors Journal,7(5):611–618, May 2007.

[4] Y.-J. Wen and A.M. Agogino. Wireless networked lighting systems foroptimizing energy savings and user satisfaction. In Proc. IEEE Wireless

Hive Networks Conf erence, pages 1–7, Aug. 2008.[5] J.J. Evans. Wireless sensor networks in electrical manufacturing. In

Proc. Electrical Insulation Conference and Electrical Manufacturing Expo, pages 460–465, Oct. 2005.

[6] V.C. Gungor and G.P. Hancke. Industrial wireless sensor networks:Challenges, design principles, and technical approaches. IEEE Trans.on Industrial Electronics, 56(10):4258–4265, Oct. 2009.

[7] A.C. Caputo and P.M. Pelagagge. Upgrading mixed ventilation systemsin industrial conditioning. Applied Thermal Engineering (Elsevier),29(14-15):3204–321 1, 2009.

[8] W. Dong, C. Chen, X. Liu, K. Zheng, R. Chu, and J. Bu FIT: AFlexible, Lightweight, and Real-Time Scheduling System for Wireless

Sensor Platforms. I EEE Trans. on Parallel and Distributed Systems,21(1):126–138, 2010.[9] A. Deshpande, C. Guestrin, and S. Madden. Resource-aware wireless

sensor-actuator networks. IEEE Data Engineering, 18(1):40–47, 2005.[10] Isaac L. Flory IV. H igh-Intensity Discharge Industrial Lighting Design

Strategies for the M inimization of Energy Usage and Life-Cycle Cost .PhD thesis, Virginia Polytechnic Institute and State University, 2008.

[11] V.C. Gungor and F. Lambert. A survey on communication networksfor electric system automation. Computer Networks Journal (Elsevier),50(7):877–897, 2006.

[12] P.E. Guerrero, D. Jacobi, and A. Buchmann. Workflow support forwireless sensor and actor networks: a position paper. In Proc. 4thworkshop on Data management for sensor networks (ACM DMSN’07),pages 31–36, 2007.

[13] G.-P. Liu, Y. Xia, J. Chen, D. Rees, and W. Hu. Networked predictivecontrol of systems with random network delays in both forward andfeedback channels. IEEE Trans. on Industrial Electronics, 54(3):1282–

1297, Jun. 2007.[14] T. Li and Y. Fujimoto. Control system with high-speed and real-

time communication links. IEEE Trans. on Industrial Electronics,55(4):1548–1557, Apr. 2008.

[15] F. Gil-Castineira, F. J. Gonzalez-Castano, and L. Franck. Extendingvehicular can fieldbuses with delay-tolerant networks. IEEE Trans. on

Industrial Electronics, 55(9):3307–3314, Sept. 2008.[16] R. Vedantham. Energy-Efficient Network Protocols for Wireless Sensor

and Actor Networks. PhD thesis, School of Electrical and ComputerEngineering, Georgia Institute of Technology, Dec. 2006.

[17] V.C. Gungor, O.B. Akan, and I.F. Akyildiz. A real-time and reliabletransport (RT )2 protocol for wireless sensor and actor networks.

IEEE/ACM Trans. on Networking, 16(2):359–370, Apr. 2008.[18] IEEE Computer Society. Wireless medium access control (MAC) and

physical layer (PHY) specifications for low-rate wireless personal areanetworks (WPANs). IEEE Sandard 802.15.4-2006, 2006.

8

PDFill PD F E

d itor w ith F

ree Writer

and Too ls







































































































11

[19] J. Chen, X. Cao, Y. Xiao, and Y. Sun. Simulated annealing foroptimisation with wireless sensor and actuator networks. IET Electronics

Letters, 44(20):1208–1209, 2008.[20] L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla, and S.S. Sastry.

Foundations of control and estimation over lossy networks. Proceedingsof the IEEE , 95(1):163–187, Jan. 2007.

[21] M. Epstein, L. Shi, A. Tiwari, and R. M Murray. Probabilisticperformance of state estimation across a lossy network. Automatica,44(12):3046–3053, 2008.

[22] X. Cao, J. Chen, C. Gao, and Y. Sun An optimal control method for

applications using wireless sensor/actuator networks. Computers and Electrical Engineering (Elsevier), 35(5):748–756, 2009.

[23] R. D’Andrea and G.E. Dullerud. Distributed control design for spatiallyinterconnected systems. IEEE Trans. on Automatic Control, 48(9):1478–1495, Sep. 2003.

[24] X. Cao, J. Chen, Y. Xiao, and Y. Sun. Distributed collaborative controlusing wireless sensor and actuator networks. In Proc. 2nd Interna-tional Conf. on Future Generation Communication and Networking(FGCN’08), volume 1, pages 3–6, Dec. 2008.

[25] P. Neumann. Communication in industrial automation-what is going on?Control Engineering Practice (Elsevier), 15(11):1332–1347, Nov. 2007.

[26] B. Sinopoli, C. Sharp, L. Schenato, S. Schaffert, and S.S. Sastry.Distributed control applications within sensor networks. Proceedingsof the IEEE , 91(8):1235–1246, Aug. 2003.

[27] X. Liu and A.J. Goldsmith. Wireless network design for distributedcontrol. In Proc. 43rd IEEE Conf. on Decision and Control, 2004.

[28] P. Marti, J. Yepez, M. Velasco, R. Villa, and J.M. Fuertes. Managing

quality-of-control in network-based control systems by controller andmessage scheduling co-design. IEEE Trans. on Industrial Electronics,51(6):1159–1167, Dec. 2004.

[29] X. Cao, J. Chen, Y. Xiao, and Y. Sun. Building environment controlwith wireless sensor and actuator networks: Centralized vs. distributed.

IEEE Trans. on Industrial Electronics, DOI:10.1109/TIE.2009.2029585,to appear.

[30] G. Welch and G. Bishop. An introduction to the kalman filter. Technicalreport, TR 95-041, Department of Computer Science, University of North Carolina, 2002.

[31] B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M.I. Jordan, andS.S. Sastry. Kalman filtering with intermittent observations. IEEE Trans.on Automatic Control, 49(9):1453–1464, Sep. 2004.

[32] R. Olfati-Saber. Distributed kalman filtering for sensor networks. InProc. 46th IEEE Conf. on Decision and Con trol, Dec. 2007.

[33] R. Carli, A. Chiuso, L. Schenato, and S. Zampieri. Distributed kalmanfiltering based on consensus strategies. IEEE Journal on Selected Areas

in Communications, 26(4):622–633, 2008.[34] L. Schenato. Optimal estimation in network ed control systems subject

to random delay and packet drop. IEEE Trans. on Automatic Control,53(5):1311–1317, Jun. 2008.

[35] V. Gupta, N.C. Martins, and J.S. Baras. Optimal output feedback control using two remote sensors over erasure channels. IEEE Trans.on Automatic Control, 54(7):1463–1476, Jul. 2008.

Jiming Chen (M’08) received Ph.D degree in Con-trol Science and Engineering from Zhejiang Univer-sity in 2005. He was a visiting scholar at INRIA,NUS. He is an associate professor with Instituteof Industrial Process Control, and the coordinatorof group of Networked Sensing and Control in theState Key laboratory of Industrial Control Tech-nology at Zhejiang University, China. Currently healso is a visiting researcher with the Centre forWireless Communications, Department of Electricaland Computer Engineering, University of Waterloo,

Canada. His research interests are estimation and control over sensor network,sensor and actuator network, target tracking in sensor networks, optimizationin mobile sensor network. He has published over 50 peer-reviewed papers. Hecurrently servers associate editor for International Journal of CommunicationSystem (Wiley), Ad Hoc & Sensor Wireless Networks, an InternationalJournal, etc. He also serves guest editor for IEEE Transaction on AutomaticControl, Wireless Communication and Mobile Computing (Wiley), etc. Heserves as a general symposia Co-Chair of ACM IWCMC 2009 and ACMIWCMC 2010, WiCON 2010 MAC track Co-Chair, Chinacom 2010 PublicityCo-Chair, and TPC for IEEE ICDCS 2010, IEEE Globecom, IEEE ICC, etc.

Xianghui Cao (S’08) received the B.S. degree in au-tomation from Zhejiang University, China, in 2006,when he also graduated from the Chukochen HonorsCollege, Zhejiang University. He is currently a PhDcandidate in the Department of Control Science andEngineering, Zhejiang University. From Dec. 2007to Jun. 2009, He was a Visiting Scholar in theDepartment of Computer Science, The Universityof Alabama. He was a reviewer for several journalsincluding IEEE Trans. on Industrial Electronics. He

served as TPC member for IEEE WiMob 2009. Hisresearch areas include networked estimation and control, distributed controlwith wireless sensor/actuator networks.

Peng Cheng received the B.E. degree in Automa-tion, and the Ph.D. degree in Control Science andEngineering in 2004 and 2009 respectively, bothfrom Zhejiang University, Hangzhou, P.R. China.He is currently working as a Postdoctoral researcherin the State Key Laboratory of Industrial ControlTechnology, Zhejiang University. His research inter-ests include robust control, nonlinear systems and

networked estimate and control.

Yang Xiao (S’98-M’01-SM’04) worked in indus-try as a MAC (Medium Access Control) architectinvolving the IEEE 802.11 standard enhancementwork before he joined academia. He is currently withDepartment of Computer Science at The Universityof Alabama. He was a voting member of IEEE802.11 Working Group from 2001 to 2004. He isan IEEE Senior Member. He currently serves asEditor-in-Chief for International Journal of Secu-

rity and Networks (IJSN), International Journal of Sensor Networks (IJSNet), and International Journal

of Telemedicine and Applications (IJTA). He serves as an associate editorfor several journals, e.g., IEEE Transactions on Vehicular Technology. Hisresearch areas are security, telemedicine, robot, sensor networks, and wirelessnetworks. He has published more than 300 papers in major journals, refereedconference proceedings, book chapters related to these research areas.

Youxian Sun received the Diploma from the Depart-ment of Chemical Engineering, Zhejiang University,China, in 1964. He joined the Department of Chemi-cal Engineering, Zhejiang University, in 1964. From

1984 to 1987, he was an Alexander Von HumboldtResearch Fellow, and Visiting Associate Professorat University of Stuttgart, Germany. He has been afull professor at Zhejiang University since 1988. In1995, he was elevated to an Academician of Chi-nese Academy of Engineering. His current researchinterests include modeling, control and optimization

of complex systems, robust control design and its application. He is author andco-author of 450 journal and conference papers. He is currently the director of institute of industrial process control and national engineering research centerof industrial automation, Zhejiang University. He is the President of ChineseAssociation of Automation, and also served as Vice-Chairman of IFAC Pulpand Paper Committee, and Vice-President of China Instrument and ControlSociety.

9

PDFill PD F E

d itor w ith F

ree Writer

and Too ls


















































Documents

Copy of Distributed Collaborative Control for Industrial Automa_new