Cooperative Tracking Control and Regulation for a Class of Multi-agent Systems

184 Pages·2019·4.789 MB·English

by  Hongjing Liang, Huaguang Zhang

Hongjing Liang · Huaguang Zhang
Cooperative
Tracking Control
and Regulation for a
Class of Multi-agent
Systems
Cooperative Tracking Control and Regulation
for a Class of Multi-agent Systems
Hongjing Liang Huaguang Zhang
(cid:129)
Cooperative Tracking
Control and Regulation
for a Class of Multi-agent
Systems
123
HongjingLiang HuaguangZhang
Collegeof Engineering Department ofElectrical Engineering
BohaiUniversity Northeastern University
Jinzhou,Liaoning, China Shenyang,Liaoning, China
ISBN978-981-13-8358-8 ISBN978-981-13-8359-5 (eBook)
https://doi.org/10.1007/978-981-13-8359-5
©SpringerNatureSingaporePteLtd.2019
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To My Family
Hongjing Liang
To My Family
Huaguang Zhang
Preface
Problem formulations of complex systems and processes can often lead to com-
munication burden, which may cause analysis and synthesis difficulties. Studies of
network scientists are necessary for the development of complex systems and
processes, which are making a dramatic progress and pushing network analysis to
itslimits.Inengineering,researchersshouldstudyhowtoassembleandcoordinate
individual physical devices into a coherent whole to perform a common task. One
effective way of representing complex systems is so-called cooperative control
method, and it also gives rise to a very active and exciting research field:
multi-agent systems. The problem of cooperative control is to design appropriate
protocols and algorithms, so that the group of agents can converge to a common
trajectory by the shared information in the presence of limited and unreliable
informationexchangeanddynamicallychanginginformationexchangetopologies.
Aconsensusalgorithmisaninteractionrulethatspecifiestheinformationexchange
between an agent and all of its neighbors on the network.
Analysisandsynthesisincludingstatefeedbackcontrol,outputfeedbackcontrol,
tracking control, load balancing in networks, rendezvous in space, formation
control, fast consensus in small-world networks, containment control, Markov
processesandgossip-basedalgorithms,clusterandobstacleavoidanceforaclassof
multi-agentsystemsareallthoroughlystudied.Thismonographmainlyinvestigates
output regulation and output containment control problem for linear multi-agent
systems. For the single-leader multi-agent systems, the following problems are
investigated in this monograph: (1) output regulation of continuous-time
state-coupled dynamics with globally reachable topologies; (2) cooperative out-
put tracking control for heterogeneous second-order discrete-time multi-agent
systems;(3)cooperativerobustoutputregulationofheterogeneouscontinuous-time
multi-agent systems; (4) cooperative put tracking problem for second-order
multi-agent systems; (5) cooperative tracking control for high-order multi-agent
systems based on reduced-order observer; (6) for discrete-time dynamics, dis-
tributed stabilized region regulator method was given; and (7) optimal output
regulation for heterogeneous multi-agent systems. At last, cooperative robust
containmentcontrolproblemwasproposedforheterogeneousmulti-agentsystems.
vii
viii Preface
Among the topics, simulation results including some typical real applications are
presented to illustrate the effectiveness and the practicability of the cooperative
control design methods proposed in the previous parts.
Jinzhou, China Hongjing Liang
Shenyang, China Huaguang Zhang
January 2019
Acknowledgements
Ouracknowledgmentsalsogotoourfellowcolleagueswhohaveofferedinvaluable
support and encouragement throughout this research effort. Thanks go to my stu-
dents,YuZhou,HuiMa,LinchuangZhang,ZhenxingZhang,YanhuiZhang,Shiyi
Zhao, and Yuanyuan Xu for their commentary. The authors are especially grateful
to their families for their encouragement and never-ending support when it was
most required. Finally, we would like to thank the editors at Springer for their
professional and efficient handling of this project.
The writing of this book was partially supported by the National Natural
ScienceFoundationofChina(61703051,61627809,61433004,61621004),andthe
Ph.D. Start-up Fund of Liaoning Province (20170520124).
ix
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Graph Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Directed Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Undirected Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Publication Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Output Regulation of State-Coupled Dynamics with Globally
Reachable Topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Problem Formulation and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1 Algebraic Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Solution of Regulator Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Robust Output Regulation for Multi-agent Systems. . . . . . . . . . . . . . . . 24
5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Cooperative Output Tracking Control for Heterogeneous
Second-Order Discrete-Time Multi-agent Systems . . . . . . . . . . . . . . . . . 31
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2 Output Synchronization for Unmeasurable Double-Integral
Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1 Basic Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Distributed Observer Design and Main Result . . . . . . . . . . . . . . . 34
3 Cooperative Output Tracking for Second-Order Discrete-Time
Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 Distributed Dynamic Feedback Design for the Output
Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
xi
xii Contents
5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Cooperative Output Regulation of Heterogeneous Continuous-Time
Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 Output Regulation of Heterogeneous Certain Multi-agent
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Cooperative Robust Output Regulation for Uncertain Networks. . . . . . . 66
5.1 Dynamic State Feedback Controller. . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Dynamic Output Feedback Controller . . . . . . . . . . . . . . . . . . . . . 72
6 Numerical Examples and Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 76
7 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Cooperative Tracking Control for High-Order Multi-agent
Systems Based on Reduced-Order Observer . . . . . . . . . . . . . . . . . . . . . 83
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2 Problem Formulation and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 84
3 Discrete-Time Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.1 Design for the Reduced-Order Observer. . . . . . . . . . . . . . . . . . . . 86
4 Extensions to Continuous-Time Multi-agent Systems . . . . . . . . . . . . . . 96
5 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.1 Distributed Control for Discrete-Time Multi-agent Systems. . . . . . 100
5.2 Example for the Continuous-Time Case. . . . . . . . . . . . . . . . . . . . 103
6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Distributed Stabilized Region Regulator for Discrete-Time
Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4 Extensions to Uncertain Multi-agent Systems . . . . . . . . . . . . . . . . . . . . 118
5 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Optimal Output Regulation for Heterogeneous Multi-agent
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128