Containment for linear multi-agent systems with exogenous disturbances

Brief Papers

Containment for linear multi-agent systems

with exogenous disturbances

Chengjie Xu a,b,Ying Zheng b,c,n,Housheng Su b,c,Hong-bin Zeng d

a School of Science,Hunan University of Technology,Zhuzhou412008,PR China

b School of Automation,Huazhong University of Science and Technology,Wuhan430074,PR China

c Key Laboratory of Education Ministry for Image Processing an

d Intelligent Control,Huazhong University of Scienc

e and Technology,Wuhan430074,

PR China

d School of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou412008,PR China

a r t i c l e i n f o

Article history:

Received11August2014

Received in revised form

8December2014

Accepted6February2015

Communicated by Guang Wu Zheng

Available online5March2015

Keywords:

Containment

Linear multi-agent systems

Exogenous disturbances

Disturbance observer

a b s t r a c t

This paper investigates containment for linear multi-agent systems(LMAS)with exogenous disturbances

under?xed topologies.Both state feedback and output feedback control protocols are proposed,under

which all the followers will asymptotically converge to the convex hull spanned by the https://www.360docs.net/doc/1612129248.html,ing

tools from matrix,graph and Lyapunov stability theories,suf?cient conditions for containment of linear

multi-agent systems with exogenous disturbances are obtained by designing exogenous disturbance

observers.Finally,numerical simulations are presented to illustrate the theoretical?ndings.

&2015Elsevier B.V.All rights reserved.

1.Introduction

In recent years,distributed cooperative control of multi-agent

systems has attracted much attention for its broad potential

applications in sensor networks,combat intelligence,surveillance,

etc.[1].Lots of works have been reported including formation

control[2,3],?ocking[4–6],leaderless consensus[7–9],leader-

following consensus[10–12],containment[13–26],and so forth.

Consensus is one of the most fundamental problems in dis-

tributed cooperative control,which means that the state of the

agents reaches an agreement on a common physical quantity of

interest by implementing an appropriate consensus protocol based

on the information from local neighbors.According to the number

of leaders,consensus problem and its extensions can be roughly

classi?ed into leaderless consensus(there is no leader in the

network),consensus tracking or leader-following consensus(there

is only one leader in the network),containment control(multiple

leaders case)[13].

Containment control for multi-agent systems with multiple

leaders has been intensively investigated for the past several years.

Under?xed topology,for guaranteeing that all the follower agents

asymptotically converge into the convex hull formed by multiple

stationary/moving leaders,a hybrid control protocol based on the

stop-and-go strategy was proposed[14].Distributed containment

control for multi-agent systems with single/double-integrator

dynamics was investigated in the presence of multiple stationary or

dynamic leaders under?xed and switching directed topologies,

respectively[15,16].Distributed?nite-time attitude containment con-

trol was studied for multiple rigid bodies[17].Necessary and suf?cient

conditions were established for containment of multi-agent systems

with stationary or dynamic leaders via both continuous and sampled

control protocols[18].Distributed containment control with multiple

dynamic leaders was studied for double-integrator dynamics under

the constraints that the velocities and the accelerations of the agents

are not available[19].Based on sample-data control protocol,neces-

sary and suf?cient containment conditions were obtained for second-

order multi-agent systems without velocity measurement[20].Impul-

sive containment for second-order multi-agent systems under a

directed network topology was investigated[21].And the containment

was investigated for multi-agent systems with heterogeneous

dynamics[22].Distributed containment was studied for second-

order multi-agent systems with inherent nonlinear dynamics[23],in

which an adaptive containment protocol was proposed.Considering

that linear system can model more natural dynamics in reality,the

containment control for general linear multi-agent systems(LMAS)

began to be discussed.A state feedback protocol was proposed by

solving an algebraic Riccati equation[24].Both output feedback and

state feedback protocols were proposed for containment of linear

Contents lists available at ScienceDirect

journal homepage:https://www.360docs.net/doc/1612129248.html,/locate/neucom

Neurocomputing

https://www.360docs.net/doc/1612129248.html,/10.1016/j.neucom.2015.02.008

0925-2312/&2015Elsevier B.V.All rights

reserved.

n Corresponding author.

E-mail address:zyhidy@https://www.360docs.net/doc/1612129248.html,(Y.Zheng).

Neurocomputing160(2015)206–212

multi-agent systems [25].The semi-global containment control for general linear multi-agent systems with input saturation was studied [26].

However,external disturbances widely exist in real processes,which is a main source of instability and poor performance.Thereby,this paper focuses the containment for linear multi-agent systems (LMAS)with exogenous disturbances.The consen-sus of multi-agent systems with disturbances has been studied by many researchers [27–29].The adaptive consensus problem of multi-agent systems with partly unknown parameters and bounded external disturbances is studied by adopting the model reference adaptive control method and an adaptive disturbance compensator in [27].By proposing a distributed protocol using the neighbors'measured outputs,output consensus problem of direc-ted networks of multiple high-order agents with external distur-bances is studied [28].The consensus of second-order multi-agent dynamical systems with exogenous disturbances is studied by designing disturbance-observer-based consensus protocol [29].Motivated by [29,30],disturbance-observer-based containment protocol is used to compensate for the in ?uence of the exogenous disturbances.When the state can be used,a state feedback control protocol is designed based on a state feedback disturbance-obs-erver.While the state cannot be used,an output feedback control protocol is designed based on an output feedback disturbance-observer.The main contribution of this paper is as follows:(1)The plant in this paper is general linear dynamic,which can be used model more real plants.(2)Output feedback containment protocol based disturbance-observer is proposed in this paper,which is more dif ?cult and more practical than the state feedback case.(3)Disturbance-observer is used for disturbance attenuation.

The rest of the paper is organized as follows.In Section 2,we state the model considered in the paper and give some basic de ?nitions,lemmas and assumptions.In Section 3,both state feedback and output feedback containment protocol based disturbance-observer are proposed,and suf ?cient containment conditions are obtained.Numerical examples are given in Section 4.Finally,we conclude the paper in Section 5.

2.Preliminaries and model description

In this section,some notations and preliminaries are intro-duced.The following notations are used throughout this paper.I n denotes the n ?n identity matrix.For a matrix A (or a vector x ),A T (or x T )represents the transpose of A (or x ).

Let G ?eV ;E ;A Tbe a directed graph with a nonempty set of nodes V ?eυ1;υ2;…;υN tM T,a set of edges E D V ?V ,and a weighted adjacent matrix A ??a ij .An edge is denoted by eυi ;υj Tin a directed graph which means that vertex j can obtain informa-tion from vertex i ,but not necessarily vice versa.a ij represents the weight of the edge eυj ;υi Tand a ij 40?eυj ;υi TA E .Node v j is called the parent node,node v i is the child node,and v j is a neighbor of v i .The neighbor set N i ?f υj eυj ;υi T A E g .A graph is undirected if eυj ;υi TA E implies eυi ;υj TA E .A directed path is a sequence of edges in a directed graph of the form eυ1;υ2T;eυ2;υ3T;…,where υj A V .The Laplacian matrix L ??l ij A R eN tM T?eN tM Tis de ?ned as

l ii ?P N tM

j ?1;j a i a ij and l ij ?àa ij ;i a j .

For a multi-agent system,an agent is called leader if the agent has no neighbor,and an agent is called follower if the agent has at least one neighbor.Assume that there are N follower agents,labeled as 1;2;…;N ,and M leaders,labeled as N t1;N t2;…;N tM .Denote the set of followers as F and the set of leaders as R .Noting that the leaders have no neighbors,L can be rewritten as L 1L 2

00

!:

The dynamics of the i th agent are described by _x

i et T?Ax i et TtB eu i et Ttωi et TT;y i et T?Cx i et TtD ωi et T;

e1T

where x i et TA R n ,u i et TA R m ,ωi et TA R m and y i et TA R p are the state,control input,bounded exogenous disturbance and the output of the i th follower agent,respectively.And A A R n ?n ,B A R n ?m ,C A R p ?n ,D A R p ?n are constant matrices.Suppose that the distur-bance ωi et T,i ?1;…;N ,is generated by the following linear exogenous system:_ξi et T?E ξi

et T;ωi et T?F ξi et T;

e2T

where ξi et TA R l denotes the state of the exogenous system,E A R l ?l and F A R m ?l are the matrices of the disturbance system.

De ?nition 1(Li et al.[19]).Let C be a subset of R n ,the set C is said to be convex if for any x and y in C and any αA ?0;1 ,the point e1àαTx tαy A C .The convex hull of a set of points X ?f x 1;x 2;…;x n g is the minimal convex set containing all points in X .We denote the convex hull of X as Co(X ).

Assumption 1.Suppose that the edges between the followers are undirected,i.e.,all the followers can access each other's informa-tion.Moreover,for each follower,there exists at least one leader that has a directed path to that follower.

Assumption 2.The matrix pair eA ;B Tis stabilizable.

Remark 1(Liu et al.[24]).Under Assumption 2,there is a unique symmetric matrix P 40that solves the following algebra Riccati equation:

A T P tPA àPB

B T P tI ?0:

e3T

Lemma 1(Li et al.[25]).Under Assumption 1,L 1is positive de ?nite,

each entry of àL à11L 2is nonnegative,and each row of àL à1

1L 2has a sum equal to one.3.Main results

In this section,the distributed containment control problem

with exogenous disturbances will be solved in virtue of distur-bance observers,i.e.,to design distributed containment protocols to ensure that all the followers can be driven into the convex hull spanned by the leaders asymptotically.

3.1.Containment of LMAS with disturbances via state feedback control

In this subsection,distributed containment protocol is pro-posed to drive the followers into the convex hull spanned by the leaders via state feedback control.A disturbance observer is designed as follows:

_η

i ?eE tHBF Teηi àHx i TtH eAx i tBu i T;^ξi ?ηi

àHx i ;^ω?F ^ξi

;e4T

where ηi A R l ?l is the internal state variable of the observer,^ξi

and ^ω

are the estimated values of ξi and ωi ,respectively.H A R l ?n is the gain matrix of the observer.Denoting e i ?ξi à^ξi

,from (2)and (4),we have _e

i ?eE tHBF Te i :e5T

Remark 2.Noting that _

^ξi ?eE tHBF T^ξi àHBF ξi ;C.Xu et al./Neurocomputing 160(2015)206–212207

_ξi ?E ξi

;BF ξi ?_x i àAx i àBu i ;e i ?ξi à^ξi

;e6T

we can get the form of the observers (4),which can guarantee that

the errors of observers converge to 0under the assumption that E tHBF is Hurwitz.

Consider the following distributed containment control proto-col:

u i ?K X

j A N i

a ij ex i àx j TàF ^ξi

;i ?1;2;…;N ;e7Twhere K is the gain to be designed.Noting that ξi ?0;a ij ?0for

i ?N t1;N t2;…;N tM ,one can conclude that _^x i

?A ^x i and u i ?0for i ?N t1;N t2;…;N tM .Let x f ?ex T 1;x T 2;…;x T N TT

;x l ?ex T N t1;

x T N t2;…;x T N tM TT ,and e ?ee T 1

;…;e T

N T,we have _x i ?Ax i tBK X

j A N i

a ij ex i àx j TàBFe i ;i ?1;2;…;N ;

_x

i ?Ax i ;i ?N t1;N t2;…;N tM ;_e

i ?eE tHBF Te i ;i ?1;2;…;N :e8T

Theorem 1.Suppose Assumptions 1and https://www.360docs.net/doc/1612129248.html,ing control protocol (6)for (1),all the followers will converge to the convex hull spanned by the leaders and the errors of disturbance observers converge to 0asymptotically if

(i)E tHBF is Hurwitz ;

(ii)K ?àe1=λ1TB T P ,where P 40is the unique solution of the

algebra Riccati equation (3)and λ1is the minimum eigenvalue of L 1.Moreover,the ?nal states of the follower agents can be given as

lim t -1J x f teL à1

1L 2 I n Tx l J ?0.

Proof.Let δi ?P j A N i a ij ex i àx j T,i ?1;2;…;N ,and δ?eδT 1;δT

2;…;

δT N TT .According to the de ?nition of L ,one can easily conclude that

δ?eL 1 I n Tx f teL 2 I n Tx l :

e9T

Then the system (1)under containment control protocol (6)with

disturbance observer (4)can be rewritten as _δ?eeI N A TteL 1

BK TTδàeI n BF Te ;_e

?eI n eE tHBF TTe :e10T

According to Lemma 1,under Assumption 1,L 1is positive de ?nite

and of course is nonsingular.Denote the eigenvalues of L 1as λi ,i ?1;2;…;N ,then λi 40.

Consider the following Lyapunov function candidate:V eδ;e T?δT

eI N

P Tδtαe T

e ;

e11T

where αis a positive small enough constant.Differentiating V with

respect to t along (9),we have _V

?2δT eI N P T_δt2e T _e ?δT

eI N ePA tA T P TTδt2δT

eL 1 PBK Tδ

à2δT

eI N PBF Te t2e T eI N eE tHBF TTe

?eδT

e T TΥàI N PBF àI N PBF Π !δe

!

;

e12T

where Υ?I N ePA tA T P Tà2e1=λ1TeL 1 PBB T P T;Π?I N eeE t

HBF TteE tHBF TT T.According to Lemma 1,under Assumption 1,L 1is positive de ?nite,there must exist orthogonal matrix U A R N ?N such that U T L 1U ?diag eλ1;λ2;…;λN T,where 0o λ1r λ2r ?r λN .Since PBB T P is semi-positive de ?nite and λi Z λ1,according to (3),one can know Υ?I N ePA tA T P Tà2e1=λ1TeL 1 PBB T P To 0.Furthermore,

if (i)holds,Π?I N eeE tHBF TteE tHBF TT To 0.Noting that PBF is a

constant matrix,choosing αsuf ?ciently small,by virtue of Schur Complement Lemma ,one can conclude that ΥàI N PBF àI N PBF Π

o 0.This

means _V et To 0.Hence,δ-0and e -0as t -1,then

eL 1 I n Tx f teL 2 I n Tx l -0,so x f -àeL à1

1L 2 I n Tx l as t -1.

According to Lemma 1,each row of àL à1

1L 2has a sum equal to

one,then associated with De ?nition 1,àeL à1

1L 2 I n Tx l et Tis in the convex hull spanned by the leaders and errors of the disturbance observers converge to 0asymptotically,which means Theorem 1holds.□

3.2.Containment LMAS with disturbances via output feedback control

In this subsection,based on the disturbance observers,which are designed by using output information,the containment of LMAS with disturbances is solved via adaptive output feedback control.Denoting ?A 0BF E àá,C ?eCDF T,the following assumption is necessary.

Assumption 3.(A ,C )and A ;C are observable.

Remark 3.Under Assumption 3,there must be a symmetric

positive de ?nite matrix Q A R 2n ?2n such that AQ tQA T àC T

C o 0.Q can be solved by the LMI or algebra Riccati equation [25].When the states are not available,the observer should be designed only depending on output information,which can be described as

_^x i ?A ^x i tBu i tBF ^ξi tS X j A N i

a ij ?e^y i à^y j Tàey i ày j T ;_

^ξi ?E ^ξi tT X

j A N i

a ij ?e^y

i à^y j Tàey i ày j T ;i ?1;2;…;N ;

^d i ?F ^ξi ;i ?1;2;…;N ;

^y i ?C ^x i tDF ^ξi

;e13T

where S ,T are constant gain matrices to be designed.Then,

containment control protocol using output information can be designed as

u i ?K X

j A N i

a ij e^x i à^x j TàF ^ξi

;i ?1;2;…;N ;e14Twhere K is the gain to be designed.Noting that ξi ?0;a ij ?0for

i ?N t1;N t2;…;N tM ,one can conclude that _^x i

?A ^x i and u i ?0for i ?N t1;N t2;…;N tM .Let ~x

i ?x i à^x i ,e i ?ξi à^ξi ,under pro-tocol (13),the system (1)with disturbance observer (12)can be rewritten as

_x i ?Ax i tBK X

j A N i

a ij ?ex i àx j Tàe~x

i à~x j T tBFe i ;i ?1;2;…;N ;_x

i ?Ax i ;i ?N t1;N t2;…;N tM ;_~x i

?A ~x i tBFe i tS X

j A N i

a ij ?C e~x i à~x j TtDF ee i àe j T ;i ?1;2;…;N ;

_~x i

?A ~x i ;i ?N t1;N t2;…;N tM ;

_e i ?Ee i tT X

j A N i

a ij ?C e~x

i à~x j TtDF ee i àe j T ;i ?1;2;…;N :e15T

Theorem 2.Suppose Assumptions 1–https://www.360docs.net/doc/1612129248.html,ing control protocol (13)for (1),all the followers will converge to the convex hull spanned by the leaders and the errors of disturbance observers converge to 0

asymptotically if K ?àe1=λ1TB T P and S T àá

?àe1=λ1TQC T ,where P 40is the unique solution of the algebra Riccati equation (3),and Q 40can be solved by the following linear matrix inequality (LMI):

tT

Q à2T

o 0:

e16T

C.Xu et al./Neurocomputing 160(2015)206–212

208

Moreover ,the ?nal states of the follower agents can be given as

lim t -1J x f teL à1

1L 2 I n Tx l J ?0,where x f ;x l are de ?ned as Theorem 1.

Proof.Suppose that x f ,x l ,δi ,δare de ?ned as Theorem 1.Let

~x

f ?e~x T 1;~x T 2;…;~x T N TT ;~x l ?e~x T N t1;~x T N t2;…;~x T N tM TT ;

ζi ?

X

j A N i

a ij e~x

i à~x j T;i ?1;2;…;N ;

and

ζ?eζT 1;ζT 2;…;ζT N TT :

According to (14),we have

_x

f ?eI N A Tx f teI N BK TδàeI N BK TζteI n BF Te ;_x

l ?eI N A Tx l ;_~x f

?eI N A T~x f teI N BF Te teI N SC TζteL 1 SDF Te ;_~x l

?eI N A T~x l ;_e

?eI N E Te teI N TC TζteL 1 TDF Te :e17T

Let θ?eL 1 E Te ,similar to (6)and (7),one can obtain _δ?eI N A tL 1 BK TδàeL 1 BK TζteI N BF Tθ;_ζ?eI N A tL 1 SC TζteI N BF TθàeL 1 SDF Tθ;_θ?eeI N E TteL 1 TDF TTθteL 1

TC Tζ:e18TNoting that under Assumption 1,L 1is positive de ?nite,and each

row of àL à1

1L 2has a sum equal to one.Then there exists orthogonal matrix U such that U T L 1U ?diag eλ1;…;λN T,where λi is the i th eigenvalue of L 1with 0o λ1r ?r λN .Let ~δ

~ζ~θ

0B @1C A ?U I N 000U I N 000U I N 0B @1C A δζθ0B @1

C A :e19TAlso let ~δ?e~δT

1;

~δT 2;…;~δT N TT ;~ζ?e~ζT 1;

~ζ

T 2

;…;~ζ

T N TT and ~θ?e~θT 1;

~θ

T 2

;…;~θT N TT .Then,we have

_~δi ?eA tλi BK T~δi àλi BK ~ζi tBF ~θi ;

_~ζi _~θi !?A BF 0E ~ζi ~θi !tλi S T C DF eT~ζi ~θi

!?~A ~ζi ~θi

!tλi S T ~C ~ζi ~θi !:e20T

Moreover,if δ-0as t -1,there would be x f teL à1

1

L 2 I n Tx l -0as t -1,and then according to Lemma 1,containment for system (1)under protocol (13)can be achieved.So we will prove that δ-0as t -1based on Lyapunov

approach.

Fig.1.Topology of system (1).

?200

0200400600800

1000120014001600t(s)

x i 1

Fig.2.The ?rst component of the states in state feedback containment for system

(1).(For interpretation of the references to color in this ?gure,the reader is referred to the web version of this

paper.)

?30

?20

?10

10

20

30

t(s)

x i 3

Fig.4.The third component of the states in state feedback containment for system (1).(For interpretation of the references to color in this ?gure,the reader is referred to the web version of this paper.)

010203040

50607080t(s)

x i 2

Fig.3.The second component of the states in state feedback containment for

system (1).(For interpretation of the references to color in this ?gure,the reader is referred to the web version of this paper.)

C.Xu et al./Neurocomputing 160(2015)206–212209

Consider the following Lyapunov function candidate:V e~δ

;~ζ;~θT?X N i ?1

e~δT i

P ~δi tβ?T i Q ?i T;e21T

where ?i ?~ζi

~θi

,βis a positive constant large enough.Differen-tiating V with respect to t along (19),we have

_V ?X N i ?12~δT i

P _~δi t2β?T i Q _?i T ?

X N i ?1

e2~δT i ePA tλi PBK T~δi t2~δT i

àλi PBK

PBF

?i

t2β?T i eQ ~

A tλ

i Q

S T

~

C T?i T?

X N i ?1

~δT i PA tA T P à2λi λ1PBB T P ~δi t2~δT i λi λ1

PBB T P PBF

?i tβ?

T i

Q ~A t~A T Q à2λi λ1

~C T ~C

?i

:

e22T

According to (2)and (15),one can obtain PA tA T P à2eλi =λ1TPBB T P o 0and Q ~A t~A T Q à2eλi

=λ1T~C T ~C o 0.Choosing βsuf ?ciently large,by using Schur Complement Lemma,we can obtain _V

o 0.Hence,e~δ

;~ζ;~θT-0as t -1.Then,eδ;ζ;e T-0as t -1,which means Theorem 2holds.□4.Simulations

In this section,several simulation results are presented to illustrate the previous theoretical results.The network includes six agents and three leaders.The topology can be described in Fig.1,in which agents 1–6are followers and 7–9are leaders.In the ?gures,red lines denote the trajectories of the leaders.

Example 1.In this example,we consider the state feedback containment for system (1).Choosing matrices A ,B ,E ,F as

A ?01000

100à20B @1C

A ;

B ?001

0B @1C A ;

E ?à1

000

0:600000B @1

C A ;F ?00

1eTand H ?2000

100

à1

0B @1C

A ;

?7?6?5?4?3?2?1

0123t(s)e

i

1

024t(s)

e i

2

?5?4

?3

?2?101234t(s)

e i 3

Fig.5.Errors of the disturbances observers in state feedback containment.

?0.5

00.511.522.5

33.544.5t(s)

x i 1

Fig. 6.The ?rst component of the states in output feedback containment for system (1).(For interpretation of the references to color in this ?gure,the reader is referred to the web version of this paper.)

?1.5

?1?0.500.511.5

22.533.5t(s)

x i 2

Fig.7.The second component of the states in output feedback containment for system (1).(For interpretation of the references to color in this ?gure,the reader is referred to the web version of this paper.)

C.Xu et al./Neurocomputing 160(2015)206–212

210

solving the Algebraic Ricatti equation (3),one obtains

P ?2:73323:23521:00003:23527:84242:73321:0000

2:7332

1:2352

0B @1C A :

Then K ?à1:0000à2:7332à1:2352eT.Figs.2–4show that the containment is achieved by applying containment protocol (6)and Fig.5shows that the disturbances observer errors converge to 0asymptotically.

Example 2.In this example,we consider the output feedback containment for system (1).Choosing matrices A ,B ,C ,D ,E ,F as A ?001à5àá,B ?01àá,C ?10eT,D ?1.5,E ?0:30:20:1

à0:8àá,F ?e0:30T,solving the Algebraic Ricatti equation (3)and the LMI (15),one can obtain P ?5:29151:00001:0000

0:2915àáand

Q ?1:01700:0131à0:0199à0:00220:01310:16080:30650:0375à0:01990:30651:64000:1972à0:0022

0:0375

0:1972

0:51900B B B @1

C C C A

:

Then

K ?2:5à1:0000à2:7332eT;S ?2:5

à1:0662

0:9186

;

and T ?2:5

à0:4231

0:0751

:

Figs.6and 7show that the containment is achieved by applying containment protocol (13)and Fig.8shows that the errors of the designed disturbances observers converge to 0asymptotically.5.Conclusions

]In this paper,containment for linear multi-agent systems with exogenous disturbances under ?xed topologies is investigated.Both state feedback and output feedback control protocols are proposed,under which all the followers will asymptotically converge to the convex hull spanned by the leaders without any global information except a connection assumption.By using tools from matrix,graph and Lyapunov stability theories,suf ?cient conditions for containment of linear multi-agent systems with exogenous disturbances are obtained.Future work will be to further investigate the containment control for linear multi-agent systems with stochastic disturbances and containment control for linear multi-agent systems with con-strained communication.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Grant nos.61473129,61374139,61104140,61034006,the Program for New Century Excellent Talents in University from Chinese Ministry of Education under Grant NCET-12-0215,Natural Science Foundation of Ministry of Education in Hunan Province(12C0077).References

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.

Chengjie Xu is a doctor candidate in the School of Automation,Huazhong University of Science and Tech-nology.Since July 2009,he has been with the School of Science,Hunan University of Technology,Zhuzhou,China,where he is currently a lecturer of automatic control engineering.His research interests are multi-agent systems,process

control.

Ying Zheng received her B.S.degree in industrial electric automation engineering in 1997from Huaz-hong University of Science and Technology,China;M.S.and Ph.D.degrees in control theory and engineering in 2000and 2003from Huazhong University of Science and Technology,China,respectively.She has been a postdoctor in the Chemical Engineering Department,National Tsing-Hua University,Hsinchu,Taiwan,from 2004to 2005,and a faculty member in the Department of Control Science and Engineering,Huazhong Univer-sity of Science and Technology,Wuhan,China (associ-ate professor 2005,professor 2010).She has been involved in many projects granted by National Science

Foundation Committee of China for recent years.Her research interests include process control,data-driven method,fault diagnosis,networked control

system.

Housheng Su received the B.S.degree in automatic control and the M.S.degree in control theory and control engineering from Wuhan University of Tech-nology,Wuhan,China,in 2002and 2005,respectively,and the Ph.D.degree in control theory and control engineering from Shanghai Jiao Tong University,Shang-hai,China,in 2008.From December 2008to January 2010,he was a postdoctoral researcher with the Department of Electronic Engineering,City University of Hong Kong,Hong Kong.Since January 2010,he has been an associate professor with the Department of Control Science and Engineering,Huazhong University of Science and Technology,Wuhan,China.His research

interests lie in the areas of multi-agent coordination control theory and its applications to autonomous robotics and mobile sensor

networks.

Hong-bin Zeng received the B.S.degree in electrical engineering from Tianjin University of Technology and Education,Tianjin,China,in 2003,M.S.degree in computer science from Central South University of Forestry,Changsha,China,in 2006,and Ph.D.degree in control science and engineering from Central South University,Changsha,China,in 2012.Since July 2003,he has been with the Department of Electrical and Information Engineering,Hunan University of Technol-ogy,Zhuzhou,China,where he is currently an associate professor of automatic control engineering.Now,he is working as a postdoctoral research associate in the Department of Electrical Engineering,Yeungnam Uni-versity,Kyongsan,Korea.His current research interests are time-delay systems,neural networks and networked control systems.

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