Multi-Agent Systems: Simulation and Applications

263 Pages·2009·3.58 MB·English

by  R Tyrrell Rockafellar

Cooperative Control
of Multi-Agent
Systems
Cooperative Control
of Multi-Agent
Systems
A C O N S E N S U S R E G I O N
A P P R O A C H
Zhongkui Li (cid:127) Zhisheng Duan
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
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AUTOMATION AND CONTROL ENGINEERING
A Series of Reference Books and Textbooks
Series Editors
FRANK L. LEWIS, Ph.D., SHUZHI SAM GE, Ph.D.,
Fellow IEEE, Fellow IFAC Fellow IEEE
Professor Professor
The Univeristy of Texas Research Institute Interactive Digital Media Institute
The University of Texas at Arlington The National University of Singapore
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Robot Manipulator Control: Theory and Practice, Frank L. Lewis;
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Classical Feedback Control: With MATLAB® and Simulink®, Second Edition,
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Intelligent Diagnosis and Prognosis of Industrial Networked Systems,
Chee Khiang Pang; Frank L. Lewis; Tong Heng Lee; Zhao Yang Dong
Synchronization and Control of Multiagent Systems, Dong Sun
Subspace Learning of Neural Networks, Jian Cheng; Zhang Yi; Jiliu Zhou
Reliable Control and Filtering of Linear Systems with Adaptive Mechanisms,
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Reinforcement Learning and Dynamic Programming Using Function
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Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach,
Gang Feng
Lyapunov-Based Control of Robotic Systems, Aman Behal; Warren Dixon;
Darren M. Dawson; Bin Xian
System Modeling and Control with Resource-Oriented Petri Nets,
MengChu Zhou; Naiqi Wu
Sliding Mode Control in Electro-Mechanical Systems, Second Edition,
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Autonomous Mobile Robots: Sensing, Control, Decision Making and
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Deterministic Learning Theory for Identification, Recognition, and Control,
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Contents
Preface vii
1 Introduction and Mathematical Background 1
1.1 Introduction to Cooperative Control of Multi-Agent Systems 1
1.1.1 Consensus . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Formation Control . . . . . . . . . . . . . . . . . . . . 6
1.1.3 Flocking . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Overview of This Monograph . . . . . . . . . . . . . . . . . . 7
1.3 Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . 9
1.3.1 Notations and Definitions . . . . . . . . . . . . . . . . 9
1.3.2 Basic Algebraic Graph Theory . . . . . . . . . . . . . 11
1.3.3 Stability Theory and Technical Tools . . . . . . . . . . 16
1.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 ConsensusControlofLinearMulti-AgentSystems:Continuous-
Time Case 19
2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 State Feedback Consensus Protocols . . . . . . . . . . . . . . 21
2.2.1 Consensus Condition and Consensus Value . . . . . . 22
2.2.2 Consensus Region . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Consensus Protocol Design . . . . . . . . . . . . . . . 29
2.2.3.1 The Special Case with Neutrally Stable Agents 30
2.2.3.2 The General Case . . . . . . . . . . . . . . . 31
2.2.3.3 Consensus with a Prescribed Convergence
Rate . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Observer-Type Consensus Protocols . . . . . . . . . . . . . . 35
2.3.1 Full-Order Observer-Type Protocol I . . . . . . . . . . 35
2.3.2 Full-Order Observer-Type Protocol II . . . . . . . . . 40
2.3.3 Reduced-Order Observer-Based Protocol. . . . . . . . 41
2.4 Extensions to Switching Communication Graphs . . . . . . . 43
2.5 Extension to Formation Control . . . . . . . . . . . . . . . . 45
2.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Consensus Control of Linear Multi-Agent Systems: Discrete-
Time Case 53
3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 54
v
vi Contents
3.2 State Feedback Consensus Protocols . . . . . . . . . . . . . . 54
3.2.1 Consensus Condition . . . . . . . . . . . . . . . . . . . 55
3.2.2 Discrete-Time Consensus Region . . . . . . . . . . . . 57
3.2.3 Consensus Protocol Design . . . . . . . . . . . . . . . 59
3.2.3.1 The Special Case with Neutrally Stable Agents 60
3.2.3.2 The General Case . . . . . . . . . . . . . . . 62
3.3 Observer-Type Consensus Protocols . . . . . . . . . . . . . . 65
3.3.1 Full-Order Observer-Type Protocol I . . . . . . . . . . 65
3.3.2 Full-Order Observer-Type Protocol II . . . . . . . . . 67
3.3.3 Reduced-Order Observer-Based Protocol. . . . . . . . 68
3.4 Application to Formation Control . . . . . . . . . . . . . . . 69
3.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 H and H Consensus Control of Linear Multi-Agent Sys-
2
∞
tems 73
4.1 H Consensus on Undirected Graphs . . . . . . . . . . . . . 74
∞
4.1.1 Problem Formulation and Consensus Condition . . . . 74
4.1.2 H Consensus Region . . . . . . . . . . . . . . . . . . 77
∞
4.1.3 H Performance Limit and Protocol Synthesis . . . . 80
∞
4.2 H Consensus on Undirected Graphs . . . . . . . . . . . . . 83
2
4.3 H Consensus on Directed Graphs . . . . . . . . . . . . . . 85
∞
4.3.1 Leader-Follower Graphs . . . . . . . . . . . . . . . . . 85
4.3.2 Strongly Connected Directed Graphs . . . . . . . . . . 87
4.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5 ConsensusControlofLinearMulti-AgentSystemsUsingDis-
tributed Adaptive Protocols 93
5.1 Distributed Relative-State Adaptive Consensus Protocols . . 95
5.1.1 Consensus Using Edge-Based Adaptive Protocols . . . 96
5.1.2 Consensus Using Node-Based Adaptive Protocols . . . 100
5.1.3 Extensions to Switching Communication Graphs . . . 101
5.2 Distributed Relative-Output Adaptive Consensus Protocols . 103
5.2.1 Consensus Using Edge-Based Adaptive Protocols . . . 104
5.2.2 Consensus Using Node-Based Adaptive Protocols . . . 107
5.2.3 Simulation Examples . . . . . . . . . . . . . . . . . . . 109
5.3 Extensions to Leader-Follower Graphs . . . . . . . . . . . . . 111
5.4 Robust Redesign of Distributed Adaptive Protocols . . . . . 114
5.4.1 Robust Edge-Based Adaptive Protocols . . . . . . . . 115
5.4.2 Robust Node-Based Adaptive Protocols . . . . . . . . 119
5.4.3 Simulation Examples . . . . . . . . . . . . . . . . . . . 121
5.5 Distributed Adaptive Protocols for Graphs Containing Direct-
ed Spanning Trees . . . . . . . . . . . . . . . . . . . . . . . . 123
5.5.1 Distributed Adaptive Consensus Protocols . . . . . . . 123
Contents vii
5.5.2 Robust Redesign in the Presence of External Distur-
bances . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6 Distributed Tracking of Linear Multi-Agent Systems with a
Leader of Possibly Nonzero Input 137
6.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 138
6.2 Distributed Discontinuous Tracking Controllers . . . . . . . . 139
6.2.1 Discontinuous Static Controllers . . . . . . . . . . . . 139
6.2.2 Discontinuous Adaptive Controllers . . . . . . . . . . 142
6.3 Distributed Continuous Tracking Controllers . . . . . . . . . 144
6.3.1 Continuous Static Controllers . . . . . . . . . . . . . . 144
6.3.2 Adaptive Continuous Controllers . . . . . . . . . . . . 147
6.4 Distributed Output-Feedback Controllers . . . . . . . . . . . 152
6.5 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . 156
6.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7 Containment Control of Linear Multi-Agent Systems with
Multiple Leaders 159
7.1 Containment of Continuous-Time Multi-Agent Systems with
Leaders of Zero Inputs . . . . . . . . . . . . . . . . . . . . . 160
7.1.1 Dynamic Containment Controllers . . . . . . . . . . . 161
7.1.2 Static Containment Controllers . . . . . . . . . . . . . 164
7.2 Containment Control of Discrete-Time Multi-Agent Systems
with Leaders of Zero Inputs . . . . . . . . . . . . . . . . . . . 164
7.2.1 Dynamic Containment Controllers . . . . . . . . . . . 165
7.2.2 Static Containment Controllers . . . . . . . . . . . . . 168
7.2.3 Simulation Examples . . . . . . . . . . . . . . . . . . . 168
7.3 Containment of Continuous-Time Multi-Agent Systems with
Leaders of Nonzero Inputs . . . . . . . . . . . . . . . . . . . 170
7.3.1 Distributed Continuous Static Controllers . . . . . . . 171
7.3.2 Adaptive Continuous Containment Controllers . . . . 176
7.3.3 Simulation Examples . . . . . . . . . . . . . . . . . . . 180
7.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8 Distributed Robust Cooperative Control for Multi-Agent
Systems with Heterogeneous Matching Uncertainties 183
8.1 Distributed Robust Leaderless Consensus . . . . . . . . . . 184
8.1.1 Distributed Static Consensus Protocols . . . . . . . . 185
8.1.2 Distributed Adaptive Consensus Protocols . . . . . . . 190
8.2 Distributed Robust Consensus with a Leader of Nonzero Con-
trol Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.3 Robustness with Respect to Bounded Non-Matching Distur-
bances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
viii Contents
8.4 Distributed Robust Containment Control with Multiple Lead-
ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
9 Global Consensus of Multi-Agent Systems with Lipschitz
Nonlinear Dynamics 207
9.1 Global Consensus of Nominal Lipschitz Nonlinear Multi-Agent
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
9.1.1 Global Consensus without Disturbances . . . . . . . . 208
9.1.2 Global H Consensus Subject to External Disturbances 211
∞
9.1.3 Extensions to Leader-Follower Graphs . . . . . . . . . 214
9.1.4 Simulation Example . . . . . . . . . . . . . . . . . . . 216
9.2 RobustConsensusofLipschitzNonlinearMulti-AgentSystems
with Matching Uncertainties . . . . . . . . . . . . . . . . . . 219
9.2.1 Distributed Static Consensus Protocols . . . . . . . . 219
9.2.2 Distributed Adaptive Consensus Protocols . . . . . . . 224
9.2.3 Adaptive Protocols for the Case without Uncertainties 230
9.2.4 Simulation Examples . . . . . . . . . . . . . . . . . . . 231
9.3 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Bibliography 235
Index 251