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

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(Peking University, Beijing, China), (Peking University, Beijing, China)
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Li and Duan address typical cooperative control problems of multi-agent systems, and propose a systematic consensus region approach to designing distributed cooperative control laws. Their approach decouples the design of the feedback gain matrices of the consensus protocols from the communications graph, and can serve in a certain sense as a measure for the robustness of the consensus protocols to variations of the communication graph. By exploiting the decoupling feature, they present several distributed adaptive consensus protocols, which adaptively tunes the weights on the communication graph and can be designed by each agent in a fully distributed fashion. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Distributed controller design is generally a challenging task, especially for multi-agent systems with complex dynamics, due to the interconnected effect of the agent dynamics, the interaction graph among agents, and the cooperative control laws.Cooperative Control of Multi-Agent Systems: A Consensus Region Approach offers a systematic framework for designing distributed controllers for multi-agent systems with general linear agent dynamics, linear agent dynamics with uncertainties, and Lipschitz nonlinear agent dynamics.

Beginning with an introduction to cooperative control and graph theory, this monograph:

  • Explores the consensus control problem for continuous-time and discrete-time linear multi-agent systems
  • Studies the H8 and H2 consensus problems for linear multi-agent systems subject to external disturbances
  • Designs distributed adaptive consensus protocols for continuous-time linear multi-agent systems
  • Considers the distributed tracking control problem for linear multi-agent systems with a leader of nonzero control input
  • Examines the distributed containment control problem for the case with multiple leaders
  • Covers the robust cooperative control problem for multi-agent systems with linear nominal agent dynamics subject to heterogeneous matching uncertainties
  • Discusses the global consensus problem for Lipschitz nonlinear multi-agent systems

Cooperative Control of Multi-Agent Systems: A Consensus Region Approach provides a novel approach to designing distributed cooperative protocols for multi-agent systems with complex dynamics. The proposed consensus region decouples the design of the feedback gain matrices of the cooperative protocols from the communication graph and serves as a measure for the robustness of the protocols to variations of the communication graph. By exploiting the decoupling feature, adaptive cooperative protocols are presented that can be designed and implemented in a fully distributed fashion.

Arvustused

"... offer[ s] a systematic framework for designing distributed controllers for multi-agent systems having linear agent dynamics. ... This monograph is certainly for a specialist in multi-agent systems. It will be useful to researchers and to advanced course control engineers where multi-agent systems are covered. Its useful as a reference text and it has a good bibliography." Control Technology Consortium (ACTC) E-News, May 2015 Edition

Preface vii
1 Introduction and Mathematical Background
1(18)
1.1 Introduction to Cooperative Control of Multi-Agent Systems
1(6)
1.1.1 Consensus
4(2)
1.1.2 Formation Control
6(1)
1.1.3 Flocking
7(1)
1.2 Overview of This Monograph
7(2)
1.3 Mathematical Preliminaries
9(9)
1.3.1 Notations and Definitions
9(2)
1.3.2 Basic Algebraic Graph Theory
11(5)
1.3.3 Stability Theory and Technical Tools
16(2)
1.4 Notes
18(1)
2 Consensus Control of Linear Multi-Agent Systems: Continuous-Time Case
19(34)
2.1 Problem Statement
20(1)
2.2 State Feedback Consensus Protocols
21(14)
2.2.1 Consensus Condition and Consensus Value
22(2)
2.2.2 Consensus Region
24(5)
2.2.3 Consensus Protocol Design
29(1)
2.2.3.1 The Special Case with Neutrally Stable Agents
30(1)
2.2.3.2 The General Case
31(2)
2.2.3.3 Consensus with a Prescribed Convergence Rate
33(2)
2.3 Observer-Type Consensus Protocols
35(8)
2.3.1 Full-Order Observer-Type Protocol I
35(5)
2.3.2 Full-Order Observer-Type Protocol II
40(1)
2.3.3 Reduced-Order Observer-Based Protocol
41(2)
2.4 Extensions to Switching Communication Graphs
43(2)
2.5 Extension to Formation Control
45(5)
2.6 Notes
50(3)
3 Consensus Control of Linear Multi-Agent Systems: Discrete-Time Case
53(20)
3.1 Problem Statement
54(1)
3.2 State Feedback Consensus Protocols
54(11)
3.2.1 Consensus Condition
55(2)
3.2.2 Discrete-Time Consensus Region
57(2)
3.2.3 Consensus Protocol Design
59(1)
3.2.3.1 The Special Case with Neutrally Stable Agents
60(2)
3.2.3.2 The General Case
62(3)
3.3 Observer-Type Consensus Protocols
65(4)
3.3.1 Full-Order Observer-Type Protocol I
65(2)
3.3.2 Full-Order Observer-Type Protocol II
67(1)
3.3.3 Reduced-Order Observer-Based Protocol
68(1)
3.4 Application to Formation Control
69(2)
3.5 Discussions
71(1)
3.6 Notes
72(1)
4 H∞ and H2 Consensus Control of Linear Multi-Agent Systems
73(20)
4.1 H∞ Consensus on Undirected Graphs
74(9)
4.1.1 Problem Formulation and Consensus Condition
74(3)
4.1.2 H∞ Consensus Region
77(3)
4.1.3 H∞ Performance Limit and Protocol Synthesis
80(3)
4.2 H2 Consensus on Undirected Graphs
83(2)
4.3 H∞ Consensus on Directed Graphs
85(7)
4.3.1 Leader-Follower Graphs
85(2)
4.3.2 Strongly Connected Directed Graphs
87(5)
4.4 Notes
92(1)
5 Consensus Control of Linear Multi-Agent Systems Using Distributed Adaptive Protocols
93(44)
5.1 Distributed Relative-State Adaptive Consensus Protocols
95(8)
5.1.1 Consensus Using Edge-Based Adaptive Protocols
96(4)
5.1.2 Consensus Using Node-Based Adaptive Protocols
100(1)
5.1.3 Extensions to Switching Communication Graphs
101(2)
5.2 Distributed Relative-Output Adaptive Consensus Protocols
103(8)
5.2.1 Consensus Using Edge-Based Adaptive Protocols
104(3)
5.2.2 Consensus Using Node-Based Adaptive Protocols
107(2)
5.2.3 Simulation Examples
109(2)
5.3 Extensions to Leader-Follower Graphs
111(3)
5.4 Robust Redesign of Distributed Adaptive Protocols
114(9)
5.4.1 Robust Edge-Based Adaptive Protocols
115(4)
5.4.2 Robust Node-Based Adaptive Protocols
119(2)
5.4.3 Simulation Examples
121(2)
5.5 Distributed Adaptive Protocols for Graphs Containing Directed Spanning Trees
123(12)
5.5.1 Distributed Adaptive Consensus Protocols
123(6)
5.5.2 Robust Redesign in the Presence of External Disturbances
129(6)
5.6 Notes
135(2)
6 Distributed Tracking of Linear Multi-Agent Systems with a Leader of Possibly Nonzero Input
137(22)
6.1 Problem Statement
138(1)
6.2 Distributed Discontinuous Tracking Controllers
139(5)
6.2.1 Discontinuous Static Controllers
139(3)
6.2.2 Discontinuous Adaptive Controllers
142(2)
6.3 Distributed Continuous Tracking Controllers
144(8)
6.3.1 Continuous Static Controllers
144(3)
6.3.2 Adaptive Continuous Controllers
147(5)
6.4 Distributed Output-Feedback Controllers
152(4)
6.5 Simulation Examples
156(2)
6.6 Notes
158(1)
7 Containment Control of Linear Multi-Agent Systems with Multiple Leaders
159(24)
7.1 Containment of Continuous-Time Multi-Agent Systems with Leaders of Zero Inputs
160(4)
7.1.1 Dynamic Containment Controllers
161(3)
7.1.2 Static Containment Controllers
164(1)
7.2 Containment Control of Discrete-Time Multi-Agent Systems with Leaders of Zero Inputs
164(6)
7.2.1 Dynamic Containment Controllers
165(3)
7.2.2 Static Containment Controllers
168(1)
7.2.3 Simulation Examples
168(2)
7.3 Containment of Continuous-Time Multi-Agent Systems with Leaders of Nonzero Inputs
170(12)
7.3.1 Distributed Continuous Static Controllers
171(5)
7.3.2 Adaptive Continuous Containment Controllers
176(4)
7.3.3 Simulation Examples
180(2)
7.4 Notes
182(1)
8 Distributed Robust Cooperative Control for Multi-Agent Systems with Heterogeneous Matching Uncertainties
183(24)
8.1 Distributed Robust Leaderless Consensus
184(13)
8.1.1 Distributed Static Consensus Protocols
185(5)
8.1.2 Distributed Adaptive Consensus Protocols
190(7)
8.2 Distributed Robust Consensus with a Leader of Nonzero Control Input
197(5)
8.3 Robustness with Respect to Bounded Non-Matching Disturbances
202(3)
8.4 Distributed Robust Containment Control with Multiple Leaders
205(1)
8.5 Notes
205(2)
9 Global Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics
207(28)
9.1 Global Consensus of Nominal Lipschitz Nonlinear Multi-Agent Systems
208(11)
9.1.1 Global Consensus without Disturbances
208(3)
9.1.2 Global H∞ Consensus Subject to External Disturbances
211(3)
9.1.3 Extensions to Leader-Follower Graphs
214(2)
9.1.4 Simulation Example
216(3)
9.2 Robust Consensus of Lipschitz Nonlinear Multi-Agent Systems with Matching Uncertainties
219(13)
9.2.1 Distributed Static Consensus Protocols
219(5)
9.2.2 Distributed Adaptive Consensus Protocols
224(6)
9.2.3 Adaptive Protocols for the Case without Uncertainties
230(1)
9.2.4 Simulation Examples
231(1)
9.3 Notes
232(3)
Bibliography 235(16)
Index 251
Zhongkui Li holds a BS from the National University of Defense Technology, Changsha, China and a Ph.D from Peking University, Beijing, China. He is currently an assistant professor in the Department of Mechanics and Engineering Science, College of Engineering, Peking University, China. Previously he was a postdoctoral research associate at the Beijing Institute of Technology, and held visiting positions at City University of Hong Kong, China and Nanyang Technological University, Singapore. He was the recipient of the Natural Science Award (First Prize) from the Ministry of Education of China in 2011 and the National Excellent Doctoral Thesis Award of China in 2012. His article (coauthored with Z.S. Duan and G.R. Chen) received the 2013 IET Control Theory & Applications Premium Award (Best Paper).

Zhisheng Duan holds an MS from Inner Mongolia University, Hohhot, China, and a Ph.D from Peking University, Beijing, China. He is currently a Cheung Kong scholar at Peking University, and is with the Department of Mechanics and Engineering Science, College of Engineering. Previously he was a postdoctor with Peking University; a visiting professor with Monash University, Melbourne, Australia; and a visiting professor with City University of Hong Kong, China. He has been the recipient of the Chinese Control Conference Guan Zhao-Zhi Award and the Natural Science Award (First Prize) from the Ministry of Education of China. He obtained the outstanding National Natural Science Foundation in China, and was selected into the Program for New Century Excellent Talents in Universities by the Ministry of Education of China. He has published over 100 papers in, and been an associate editor and advisory board member of, numerous international referred journals and conferences.
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