A unified approach to output synchronization of heterogeneous multi-agent systems via L2-gain design

Shan ZUO,Yongduan SONG,Hamidreza MODARES,Frank L.LEWIS,Ali DAVOUDI

1.School of Automation Engineering,University of Electronic Science and Technology of China,Chengdu Sichuan 611731,China;

2.The University of Texas at Arlington Research Institute,Fort Worth,TX 76118,U.S.A.

A unified approach to output synchronization of heterogeneous multi-agent systems via L2-gain design

Shan ZUO1,2?,Yongduan SONG1,Hamidreza MODARES2,Frank L.LEWIS2,Ali DAVOUDI2

1.School of Automation Engineering,University of Electronic Science and Technology of China,Chengdu Sichuan 611731,China;

2.The University of Texas at Arlington Research Institute,Fort Worth,TX 76118,U.S.A.

In this paper,a unified design procedure is given for output synchronization of heterogeneous multi-agent systems(MAS)on communication graph topologies,using relative output measurements from neighbors.Three different control protocols,namely,full-state feedback,static output-feedback,and dynamic output-feedback,are designed for output synchronization.It is seen that a unified design procedure for heterogeneous MAS can be given by formulation and solution of a suitable local L2-gain design problem.Sufficient conditions are developed in terms of stabilizing the local agents’dynamics,satisfying a certain small-gain criterion,and solving the output regulator equations.Local design procedures are presented for each agent to guarantee that these sufficient conditions are satisfied.The proposed control protocols require only one copy of the leader’s dynamics in the compensator,regardless of the dimensions of the outputs.This results in lower-dimensional compensators for systems with high-order outputs,compared to the p-copy internal model approach.All three proposed control protocols are verified using numerical simulations.

Heterogeneous systems,output-feedback,output synchronization,small-gain theorem

1 Introduction

Distributed control protocols of multi-agent systems(MAS)studied in[1–6]assure that all agents reach agreement on certain quantities of interests(leaderless consensus)or follow the trajectory of a leader node(leader follower consensus).A rich body of literature has been developed on state synchronization of homogeneous MAS,in which all agents have identical dynamics[7–11].

However,in many practical applications,the agents are heterogeneous in that the dynamics and even statespace dimensions of the agents are different.For these systems,state synchronization is meaningless.Therefore,distributed output synchronization of heterogeneous MAS has attracted compelling attention in the literature[12–24].Controller design for heterogeneous MAS is complicated by the fact that the agents have different dynamics and so the standard Kronecker product cannot be used.The upshot is that the closed-loop dynamics has the local controller design and the global graph properties intermingled in a very complex manner.Design of suitable local distributed protocols is consequently difficult.

There are generally three main approaches to solve the leader-follower output synchronization problem for heterogeneous MAS.In the first approach,a distributed observer is first designed to estimate the leader’s state for all agents.Then,a static compensator is designed for each agent,often based on the output regulator equations[12–16].

In the second approach,the relative output information from neighbors is used to design a control protocol and the leader’s state is not estimated[17–20].The output synchronization problem is addressed in[17]under the assumption that the communication graph contains no cycle.Su et al.[18]removed the no-cycle assumption,however,the nominal dynamics of all agents are restricted to be the same.Huang et al.[19]and Yaghmaie et al.[20]solved the output synchronization problem using an H∞criterion.All of these works use the p-copy internal model principle.A dynamic compensator is designed for each agent,which incorporates a p-copy internal model of the leader’s dynamics,with pthedimension of the agents’outputs.This approach can cope with uncertainties in the agent dynamics,and does not require the solution of the output regulator equations.However,it may lead to a complicated high-dimensional compensator,which introduces redundant dynamics.This is because the compensator of each agent must essentially have p copies of the leader’s dynamics.Therefore,the compensator dimension and complexity is high if the agents have high-order outputs.

The third approach deals with the output synchronization problem for heterogeneous networks of nonintrospective agents[21–24],which do not have selfknowledge,such as their own state/output,and only possess information that is transmitted over the communication network,such as the relative output information from neighbors.A minimum-phase condition is needed.

The main idea is to first homogenize the heterogeneous network using a state transformation to obtain a dynamical model that is substantially the same as for the other agents.Then,the model differences occur only in particular locations where they can be suppressed by using high-gain observer techniques.The internal observer dynamics are constructed to estimate unmeasured states,which introduces additional computational complexity.The agents in[21–23]are assumed to exchange not only the relative output information from neighbors,but also the relative information about their internal estimates,via the communication network.Reference[24]removes the additional communication channel for exchanging controller states,based on a combination of low-and high-gain design techniques.

This paper investigates the output synchronization problem for heterogeneous MAS.Three standard control protocols using full-state feedback,static out put feedback(OPFB)and dynamic OPFB,are designed at each agent.The contributions of this paper are as follows:

.A unified approach to the design of synchronizing protocols for heterogeneous MAS,using neighbors’relative output measurements,is provided by formulation and solution of a suitable local L2-gain design problem.This L2-gain problem can be solved by local design algorithms that guarantee the local gains are bounded by a certain value depending on the global graph structure.

.The global and local sufficient conditions for the existence of the three control protocols are derived.The dynamic compensator employed in each approach incorporates only one copy of the leader’s dynamics,regardless of the dimensions of the outputs.This results in simpler and lower-dimensional compensator and controller for systems with high-order outputs,compared to the p-copy internal model principle.

.The dynamic OPFB control protocol addresses a more challenging case of heterogeneous nonintrospective agents,in which the relative output information of each agent and its neighbors,is the only available information.Compared to[21–24],our approach does not need to homogenize the heterogeneous network using a state transformation.Moreover,our approach does not need the additional communication channel for exchanging controller states via network,and is consequently computationally inexpensive.

The rest of the paper is organized as follows:In Section2,we give the preliminaries on the graph theory,and define three types of output synchronization problems for heterogeneous MAS using different control laws.In Section 3,we present our main results.Sufficient local conditions to solve the output synchronization problem with the proposed three control protocols are presented.Local design procedures are addressed,respectively.In Section 4,we give two simulation cases to illustrate our designs.Finally,in Section5we present our conclusions.

2 Preliminaries and problem formulation

2.1 Preliminaries

Suppose that the interaction among the followers is represented by a weighted graph G=(V,E,A)with a nonempty finite set of N nodes V={v1,v2,...,vN},a set of edges or arcs E?V×V,and the associated adjacency matrix A=[aij]∈ RN×N.Here,the digraph is assumed to be time-invariant,i.e.,A is constant.An edge rooted at node j and ended at node i is denoted by(vj,vi),which means information can flow from node j to node i.aijis the weight of edge(vj,vi),and aij＞0 if(vj,vi)∈E,otherwise aij=0.Node j is called a neighbor of node i if(vj,vi)∈E.The set of neighbors of node i is denoted as Ni={j|(vj,vi)∈E}.Define the in-degree matrix as D=diag{di}∈ RN×Nwithand the Laplacian matrix as L=D?A.In this paper,we consider a group of N+1 agents,composed of N followers and one leader.The leader has no incoming edges and so exhibits autonomous behavior.The followers have incoming edges and receive direct information from the neighbors.Digraph=(V,E)shows the interaction among the followers and the leader.Digraphis said to have a spanning tree,if there is a node ir(called the root),such that there is a directed path from the root to every other node in the graph.

We use the following notations throughout this paper:R represents the real domain and C represents the complex domain.is the closed right half-complex plane. ρ(X)and σ(X)are the spectral radius and the spectrum of some square matrix X.IN∈ RN×Nis the identity matrix.Kronecker product is denoted by?.The operator diag{·}builds a block diagonal matrix from its argument.

2.2 Output regulation problem

Consider N heterogeneous linear dynamical MAS

where xi∈Rniis the state,ui∈Rmiis the input,and yi∈Rpis the output for i=1,...,N.

The dynamics of a leader are given by

where S ∈ Rq×q,R ∈ Rp×qare constant matrices,ζ0(t)∈Rqis the reference state,and y0(t)∈Rpis the reference output.

The following assumptions are made in this paper:

Assumption 1The real parts of the eigenvalues of S are nonnegative.

Assumption 2is stabilizable,(Ai,Ci)is detectable,andis detectable for all i∈N.

Assumption 3

Assumption 4The directed graphhas a spanning tree with the leader as its root.

Remark 1Assumption 1 is a standard one made to avoid the trivial case of stable S.The modes associated with the eigenvalues of S with negative real parts will exponentially decay to zero and will in no way affect the asymptotic behavior of the closed-loop system.Assumption 3 can be paraphrased by saying that the transmission zeros of the followers’system(1)do not coincide with the eigenvalues of the leader’s system(2),and it is often simply called the transmission zeros condition.Assumptions 2 and 4 are standard assumptions for the output regulation problem and will be used in the main result.

The objective of the output synchronization is to design control protocols uiin(1)to assure the followers’outputs yitrack the leader’s output y0.To this end,define the output synchronization error as

The relative output information of each agent with respect to its neighbors is the only information exchanged inthecommunicationnetwork.Therefore,wedefinethe following local neighborhood output tracking error for each agent,which is a linear combination of its output relative information

This is known as relative output-feedback(OPFB).Three types of output synchronization problems for heterogeneous MAS using different control laws are defined as follows.These are standard control laws used in the literature.

Problem 1The output synchronization problem via relative OPFB and local full-state feedback is to design distributed control protocols as follows:

Problem 2The output synchronization problem via relative OPFB and local static OPFB is to design distributed control protocols as follows:

Problem 3The output synchronization problem via relative OPFB and dynamic OPFB is to design distributed control protocols as follows:

Remark 2Problem 1 requires the full state information of each agent.This information,however,may not be available in some practical applications.This issue is obviated in Problem 2 by considering a static OPFB design.Both Problems 1 and 2 require absolute values of state or output of each agent.In some applications,however,the agents are non-introspective,and the only information available to each agent is a linear combination of the relative outputs with respect to its neighbors received over the network.Problem 3 uses the dynamic OPFB design to address this issue.This solution,however,comes at the cost of a higher-order compensator and controller in(8)compared to that in(6)and(7).

The solutions to these problems rest on the following lemma.

In global form these are written as

This situation is shown in Fig.1,where

Define the local transfer functions for i∈ N as Ti(s)≡Ci(s?i)?1i.Then,the global transfer function is T(s)≡diag{Ti(s)}.

Fig.1 Closed-loop system of(10).

The next result is from[25,26].

Lemma 1Using the small-gain theorem.Systems(9)are stable for i∈N,ifiis stable and

Remark 3In Lemma 1,the small-gain theorem is used to decouple the control design at each agent from the global information of the communication graph structure,which appears in ρ(A)in(11).

3 Main results and design procedures for Problems 1–3

In this section,the sufficient local conditions for the existence of solutions to Problems 1–3 are provided.Moreover,the local design procedures are presented,respectively.It is seen that the control design for each problem depends on formulation and solution of a L2-gain design problem.

3.1 Sufficient conditions and local controller design algorithm for problem 1

Given control protocols(6),assume the graph is normalized so that

Then,(5)can be reformulated as

Systems(1)and(4),under full-state feedback controller(6),have the following closed-loop form

and xi=[xiT,ziT]T,i=[0 GiT]T,Ci=[Ci0]for all i∈N.Then,(14)can be rewritten as

The following is a main result.

Theorem 1For systems(16),suppose the following three conditions hold for each i∈N:

iii)There exists a unique solution Xito the output regulator equations

Then,Problem 1 is solved.

ProofDefine tracking error vectorsThen according to(17),one has

This gives the closed-loop tracking error dynamics as

It is seen that,if there exists a unique solution Xito(17)for each i∈N,solving Problem 1 is equivalent to stabilizing systems(20).Using Lemma 1,ifin(15)is Hurwitz,andthen systems(20)are stable.Hence,Problem 1 is solved.

This result relies on solution of the global output regulator equations(17).Next,we give a local design procedure that guarantees(17)has a unique solution.The next technical result is needed.

Lemma 2[12,Theorem 1.9]Given Assumption3,the local output regulator equations

have unique solution pairs(Πi,Γi),respectively.

The next result addresses condition iii)in Theorem 1.

Theorem 2Assume that for each i∈N,the matrixiis Hurwitz.Make Assumption 3,and let(Πi,Γi)be solutions to(21).Then,under Assumption 1,there exists a unique solution Xi=[ΠiTIq]Tto equations(17)for each i∈N,if the matrices Ki,Hi,Fi,and Giare designed as

where Kiis such that Ai+BiKiis Hurwitz,and Giis such that(S,Gi)is controllable.

ProofSee the appendix.

Remark 4Here,the control matrices’dimensions are:Fi∈ Rq×q,Gi∈ Rq×p,Ki∈ Rmi×ni,and Hi∈ Rmi×q.By contrast,the control matrices’dimensions using pcopy internal model principle are:Fi∈ Rpq×pq,Gi∈Rpq×p,Ki∈ Rmi×ni,and Hi∈ Rmi×pq.Compared to the p-copy internal model principle,our approach results in a lower-dimensional and computationally inexpensive compensator and controller for systems with high-order outputs.

Note that Theorem 2 requires the Assumption thatiis Hurwitz.The following design procedure addresses conditions i)and ii)in Theorem 1.

Based on Theorem 2,we obtain the following local design procedure to solve Problem 1.Using(22)and(20)can be reformulated as

Define measured outputs

Then,u1i=Kiwi.Now,(23)can be written as

The global closed-loop system of(26)is shown in Fig.2,where

Fig.2 Closed-loop system of(26).

Now,we give a local L2-gain design procedure for solving Problem 1.

Theorem 3(L2-gain design)Under Assumptions 1–4,select γi＜ 1/ρ(A),and design matrices Hi,Fiand Gias in Theorem 2.Then,Problem 1 is solved if,for some positive definite matrices Ri,and scalars αi＞ 0,there exist matrices Kiand Lisuch that

where PTi=Pi＞0 is the solution to

ProofBy the same process in[27],systems(26)are OPFB stabilizable with L2gain bounded by γi＜ 1/ρ(A),if and only if,condition(27)holds with a feasible solution to(28).This satisfies conditions i)and ii)in Theorem1.Design the control matrices as in(22),using Theorem 2,condition iii)in Theorem 1 also holds.Therefore,Problem 1 is solved.

Remark 5If 1ρ(A)or its estimated information is available to each agent in advance,then condition ii)in Theorem 1 is decentralized so that e/ach agent can design its controller independently.If 1ρ(A)is unknown to each agent,γican be set as small as possible.

According to[27],necessary conditions for the existence of matrices Ki,Liand Piin Theorem 3 are:

Theorem4MakeAssumptions2and3,let(S,Gi)be controllable.Then,the necessary conditions(29)hold.

ProofSee the appendix.

The procedure to solve Problem 1 is summarized in Algorithm 1.

Remark 6Motivated by[28],to reduce the effect of the disturbances to a prespecified level,we present a procedure by solving the ARE(28)for successively smaller values of the constant αi.

3.2 Sufficient conditions and local controller design algorithm for Problem 2

The full-state feedback control protocol,developed in Section 3.1,requires the complete knowledge of each agent’sstate.This requirement is obviated in this section by using the static OPFB design in(7).

Systems(1)and(4),under the static OPFB controller(7),have the following closed-loop form

Then,(30)can be rewritten as(16).Therefore,Theorem 1 holds to solve Problem 2,with the redefined matrixiin(31)and the closed-loop tracking error dynamic systems as in(20).

To obtain a local design procedure to guarantee the conditions in Theorem 1 for solving Problem 2,the following results are given.

Theorem 5Assume that for each i∈N,the matrixiin(31)is Hurwitz.Under Assumption 3,there exist unique solutions to(21).Then,under Assumption 1,there exists a unique solution Xi=[ΠiTIq]Tto(17)if the matrices Ki,Hi,Fiand Giare designed as

where Kiis such that Ai+BiKiCiis Hurwitz,and Giis such that(S,Gi)is controllable.

ProofThe proof follows that of Theorem 2 with matrices defined in(32).

Next,we obtain the following local design procedure to solve Problem 2.

Using(32),(20)can be reformulated as(24)with u1i=KiCi[Ini?Πi]εi.Define measured outputs

Now,Theorem 3 and Algorithm 1 hold for solving Problem 2 withredefined as in(33).

Remark 7The difficulties of static OPFB design are well known in the literature[29–31].In this paper,however,we show that the output regulation using fullstate feedback and static OPFB can be confronted using a similar L2-gain design algorithm.Moreover,for the static OPFB design in(7),Theorem 4 also holds.That is,under Assumptions 2 and 3,is stabilizable,and redesigned matrices=are detectable.Therefore,the necessary conditions for the existence of Ki,Li,and Piin(27)and(28)are guaranteed for solving Problem 2.

3.3 Sufficient conditions and local controller design algorithm for Problem 3

The full-state feedback and static OPFB control protocols(6)and(7)require the absolute values of state or output of each agent.In this section,a dynamic OPFB control protocol is designed,which only requires the relative OPFB information(5).

Systems(1)and(4),under dynamic OPFB controller(8),have the following closed-loop form

Then,(34)can be rewritten as(16).Therefore,Theorem 1 holds to solve Problem 3,with the redefined matrixiin(35)and the closed-loop tracking error dynamic systems as in(20).

To obtain a local design procedure to guarantee the conditions in Theorem 1 for solving Problem 3,the following results are given.

Theorem 6Make Assumptions 1–3,let(Πi,Γi)be solutions to(21).Then,the matrixin(35)is Hurwitz,and there exists a unique solution Xi=[X1iTX2iT]T=[ΠiTΠiTIq]Tto equations(17)if the matrices Fi,Giand Hiare designed as

where Hixis such that Ai+BiHixis Hurwitz,and Giis such thatis Hurwitz.

ProofSee the appendix.

Using Theorem6,we obtain the following local design procedure to solve Problem 3.

Using(36)and(37),one can reformulate(20)as

Define measured outputs

Now,(38)can be written as(26).Algorithm 1 can also be used to solve Problem 3.Moreover,since the matrices Fi,Giand Hidesigned in Theorem 6 make the system matrixHurwitz,there always exist feasible solutions to(27)and the ARE(28),with successively smaller values of αi.

4 Simulation results

Consider a group of eight followers and one leader,with the communication graphdepicted in Fig.3.Based on the communication graph,ρ(A)=0.5.Consider the followers’dynamics in(1),and the leader’s dynamics in(2),with the systems matrices defined as

Fig.3 Communication graph

Simulation case1We design the full-state feedback control for followers i=1,...,6,and the static OPFB control for followers i=7,8.Select γi=1.8 ＜ 1/ρ(A).To satisfy the hypothses of Theorem 2,the control matrices Giare chosen as

The control matrices Kifound by solving(27)and the ARE(28)are

The simulated output trajectories of all agents,and the output tracking errors of the followers in Case 1 are shown in Fig.4 and Fig.5,respectively.It is seen that the trajectories of the followers converge to the trajectory of the leader and the output tracking errors go to zero asymptotically.

Fig.4 The simulated output trajectories of all agents in Case1.

Fig.5 The output tracking errors ηiof the followers in Case1.

Simulation case 2We design the dynamic OPFB control for all followers.Select γi=1.8 ＜ 1ρ(A).To satisfy the hypotheses of Theorem 6,the control matrices Giare chosen as

The control matrices Hixfound by solving(27)and the ARE(28)are

The simulated output trajectories of all agents,and the output tracking errors of the followers in Case 2 are shown in Fig.6 and Fig.7,respectively.It is seen that the trajectories of the followers converge to the trajectory of the leader and the output tracking errors go to zero asymptotically.

Fig.6 The simulated output trajectories of all agents in Case2.

Fig.7 The output tracking errors ηiof the followers in Case2.

5 Conclusions

This paper investigates the output synchronization problem of linear heterogeneous MAS using full-state feedback,static output-feedback,and dynamic out put feed back control.With a fixed communication network that has a spanning tree,sufficient local conditions are developed in terms of stabilizing the local agents’dynamics,satisfying an small-gain criterion and solving the output regulator equations.A unified design approach for the three proposed control protocols,using relative output information from neighbors,is provided by formulating and solving a local L2-gain design problem.The effectiveness of the proposed three control protocols has been validated by the simulation case studies.

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24 May 2017;revised 27 July 2017;accepted 2 August 2017

DOIhttps://doi.org/10.1007/s11768-017-7067-0

?Corresponding author.

E-mail:shan.zuo@uta.edu.

This paper is dedicated to Professor T.J.Tarn on the occasion of his 80th birthday.

This work was supported in part by the State Key Development Program for Basic Research of China(No.2012CB215202),in part by the National Science Foundation(No.ECCS-1405173),in part by the Office of Naval Research(No.N00014-17-1-2239).

?2017 South China University of Technology,Academy of Mathematics and Systems Science,CAS,and Springer-Verlag GmbH Germany

Appendix

Proof of Theorem 2Note that the first equation in(17)is a Sylvester equation,which under Assumption 1,always has a unique solution as long asiis stable.If the above designed control laws also make Xisatisfy the second equation in(17),then the proof is completed.

Let Xi=[ΠiTIq]T,then,(17)can be expanded as

It is now required to show that under the hypotheses in the statement of this theorem,Xi=[ΠiTIq]Tis the unique solution satisfying(a1).

From(21)and(22),we can get the identities

which can be expanded as

However,(a3)and(a1)are identical.Therefore,Xi=[ΠiTIq]Tsatisfies both equations in(a1).Sinceiis Hurwitz,then,Xi=[ΠiTIq]Tis the unique solution to(a1),and hence(17).This completes the proof.

Proof of Theorem 4Given Assumption 3,Lemma 2 holds.Then,from the Roth’s removal rule[32],matricesare similar.For the pair

Using the PBH test[33],the pairis stabilizable if and only if

Since(Ai,Bi)is stabilizable,rank[Ai? λIniBi]=nifor all λ∈C+.Also,det(S?λIq)≠0 for all λ?σ(S).Thus,one has

Write M(λ)=M1(λ)M2(λ),where

Since(S,Gi)is controllable,for all λ ∈ C,M1(λ)has rank ni+q.By Assumption 3,M2(λ)has rank ni+p+q for all λ ∈ σ(S).Hence,by Sylvester’s inequality,

Combining(a6)and(a7)gives

Thus the pair(?Ai,?Bi)=is stabilizable.

Since(Ai,Ci)is detectable and(S,Gi)is controllable,similarly,using the PBH test,one can prove that(?Ai,Ci)=is detectable.Similarly,using the PBH test,one can prove that=detectable,sinceis detectable and(S,Gi)is controllable.

Therefore,design the control matrices as in(22),necessary conditions for the existence of solutions to(27)and(28)hold.

Proof of Theorem 6The first equation in(17)is a Sylvester equation.Under Assumption 1,it always has a unique solution Xias long asiis Hurwitz.If the above designed control laws makeiHurwitz,and also make Xisatisfies the second equation in(17),then the proof is completed.

Next,we prove that the unique solution Xialso satisfies the second equation of(17).Let Xi=[X1iTX2iT]T.Then,(17)can be expanded as

Let X1i= Πi,X2i=[ΠiTIq]T.Based on(36)and(37),we can get that

Using Lemma 2,under Assumption 3,the local output regulator equations in(21)have unique solutions.Now using(21),(a12)and(a13),(a11)can be reformulated as

It is seen that Xi=[ΠiTΠiTIq]Tsatisfies both equations(a14)and(a15).Since the eigenvalues ofiand S do not coincide under Assumption 1,Xi=[ΠiTΠiTIq]Tis the unique solution that satisfies(a14).By(a15),Xialso satisfies the second equation of(17).This completes the proof.

Shan ZUOreceived the B.Sc.degree in Physical Electronics from University of Electronic Science and Technology of China,Chengdu,China,in 2012.She is working toward the Ph.D.degree in the School of Automation Engineering,University of Electronic Science and Technology of China since 2012.She is currently working toward the Joint Ph.D.degree in the University of Texas at Arlington,Arlington,TX,U.S.A.since 2014,supported by the China Scholarship Council.Her research interests include distributed synchronization control,distributed containment control,microgrid systems,and smart grid.E-mail:shan.zuo@uta.edu.

Yongduan SONG(M’92-SM’10)received the Ph.D.degree in Electrical and Computer Engineering from Tennessee Technological University,Cookeville,TN,U.S.A.,in 1992.He held a tenured Full Professor position with North Carolina A&T State University,Greensboro,from 1993 to 2008 and a Langley Distinguished Professor position with the National Institute of Aerospace,Hampton,VA,from 2005 to 2008.He is now the Dean of School of Automation,Chongqing University,and the Founding Director of the Institute of Smart Systems and Renewable Energy,Chongqing University.He was one of the six Langley Distinguished Professors with the National Institute of Aerospace(NIA),Founding Director of Cooperative Systems at NIA.He has served as an Associate Editor/Guest Editor for several prestigious scientific journals.Prof.Song has received several competitive research awards from the National Science Foundation,the National Aeronautics and Space Administration,the U.S.Air Force Office,the U.S.Army Research Office,and the U.S.Naval Research Office.His research interests include intelligent systems,guidance navigation and control,bio-inspired adaptive and cooperative systems,rail traffic control and safety,and smart grid.E-mail:ydsong@cqu.edu.cn.

Hamidreza MODARESreceived the B.Sc.degree from the University of Tehran,Tehran,Iran,in 2004,the M.Sc.degree from the Shahrood University of Technology,Shahrood,Iran,in 2006,and the Ph.D.degree from The University of Texas at Arlington,Arlington,TX,U.S.A.,in 2015.He was a Senior Lecturer with the Shahrood University of Technology,from 2006 to 2009 and a Faculty Research Associate with the University of Texas at Arlington,from 2015 to 2016.He is currently an Assistant Professor in the Electrical and Computer Engineering Department,Missouri University of Science and Technology,Rolla,MO,U.S.A.His current research interests include cyber-physical systems,reinforcement learning,distributed control,robotics,and machine learning.He is an Associate Editor for the IEEE Transactions on Neural Networks and Learning Systems.He has received Best Paper Award from 2015 IEEE International Symposium on Resilient Control Systems.E-mail:modaresh@mst.edu.

FrankL.LEWISMember,NationalAcademy of Inventors.Fellow IEEE,Fellow IFAC,Fellow AAAS,Fellow U.K.Institute of Measurement&Control,PE Texas,U.K.Chartered Engineer.UTA Distinguished Scholar Professor,UTA Distinguished Teaching Professor,and Moncrief-ODonnell Chair at the University of Texas at Arlington Research Institute.Qian Ren Thousand Talents Consulting Professor,Northeastern University,Shenyang,China.He obtained the Bachelor’s degree in Physics/EE and the MSEE at Rice University,the MS in Aeronautical Engineering from Univ.W.Florida,and the Ph.D.at Ga.Tech.He works in feedback control,intelligent systems,cooperative control systems,and nonlinear systems.He is author of 7 U.S.patents,numerous journal special issues,journal papers,and 20 books,including Optimal Control,Aircraft Control,Optimal Estimation,and Robot Manipulator Control which are used as university textbooks worldwide.He received the Fulbright Research Award,NSF Research Initiation Grant,ASEE Terman Award,Int.Neural Network Soc.Gabor Award,U.K.Inst Measurement&Control Honeywell Field Engineering Medal,IEEE Computational Intelligence Society Neural Networks Pioneer Award,AIAA Intelligent Systems Award.Received Outstanding Service Award from Dallas IEEE Section,selected as Engineer of the year by Ft.Worth IEEE Section.Was listed in Ft.Worth Business Press Top 200 Leaders in Manufacturing.Texas Regents Outstanding Teaching Award 2013.He is Distinguished Visiting Professor at Nanjing University of Science&Technology and Project 111 Professor at Northeastern University in Shenyang,China.Founding Member of the Board of Governors of the Mediterranean Control Association.E-mail:lewis@uta.edu.

Ali DAVOUDI(S04-M11-SM15)received his Ph.D.in Electrical and Computer Engineering from the University of Illinois,Urbana-Champaign,IL,U.S.A.,in 2010.He is currently an Associate Professor in the Electrical Engineering Department,University of Texas,Arlington,TX,U.S.A.He is an Associate Editor for the IEEE Transactions on Transportation Electrification,the IEEE Transactions on Energy Conversion,and the IEEE Power Letters.He has received 2014 Ralph H.Lee Prize Paper Award from IEEE Transactions on Industry Applications,Best Paper Award from 2015 IEEE International Symposium on Resilient Control Systems,2014-2015 Best Paper Award from IEEE Transactions on Energy Conversion,2016 Prize Paper Award from the IEEE Power and Energy Society,and 2017 IEEE Richard M.Bass Outstanding Young Power Electronics Engineer Award.E-mail:davoudi@uta.edu.