Cooperative Control of Multi-Agent Systems: A Consensus Region Approach

263 Pages·2014·3.98 MB·English

by  Zhongkui Li

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
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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