1st Edition

Cooperative Control of Multi-Agent Systems A Consensus Region Approach

By Zhongkui Li, Zhisheng Duan Copyright 2015
    262 Pages 50 B/W Illustrations
    by CRC Press

    262 Pages 50 B/W Illustrations
    by CRC Press

    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 H∞ 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.

    Preface

    Introduction and Mathematical Background

    Introduction to Cooperative Control of Multi-Agent Systems

    Consensus

    Formation Control

    Flocking

    Overview of This Monograph

    Mathematical Preliminaries

    Notations and Definitions

    Basic Algebraic Graph Theory

    Stability Theory and Technical Tools

    Notes

    Consensus Control of Linear Multi-Agent Systems: Continuous-Time Case

    Problem Statement

    State Feedback Consensus Protocols

    Consensus Condition and Consensus Value

    Consensus Region

    Consensus Protocol Design

    Observer-Type Consensus Protocols

    Full-Order Observer-Type Protocol I

    Full-Order Observer-Type Protocol II

    Reduced-Order Observer-Based Protocol

    Extensions to Switching Communication Graphs

    Extension to Formation Control

    Notes

    Consensus Control of Linear Multi-Agent Systems: Discrete-Time Case

    Problem Statement

    State Feedback Consensus Protocols

    Consensus Condition

    Discrete-Time Consensus Region

    Consensus Protocol Design

    Observer-Type Consensus Protocols

    Full-Order Observer-Type Protocol I

    Full-Order Observer-Type Protocol II

    Reduced-Order Observer-Based Protocol

    Application to Formation Control

    Discussions

    Notes

    H∞ and H2 Consensus Control of Linear Multi-Agent Systems

    H∞ Consensus on Undirected Graphs

    Problem Formulation and Consensus Condition

    H∞ Consensus Region

    H∞ Performance Limit and Protocol Synthesis

    H2 Consensus on Undirected Graphs

    H∞ Consensus on Directed Graphs

    Leader-Follower Graphs

    Strongly Connected Directed Graphs

    Notes

    Consensus Control of Linear Multi-agent Systems Using Distributed Adaptive Protocols

    Distributed Relative-State Adaptive Consensus Protocols

    Consensus Using Edge-Based Adaptive Protocols

    Consensus Using Node-Based Adaptive Protocols

    Extensions to Switching Communication Graphs

    Distributed Relative-Output Adaptive Consensus Protocols

    Consensus Using Edge-Based Adaptive Protocols

    Consensus Using Node-Based Adaptive Protocols

    Simulation Examples

    Extensions to Leader-Follower Graphs

    Robust Redesign of Distributed Adaptive Protocols

    Robust Edge-Based Adaptive Protocols

    Robust Node-Based Adaptive Protocols

    Simulation Examples

    Distributed Adaptive Protocols for Graphs with Directed Spanning Trees

    Distributed Adaptive Consensus Protocols

    Robust Redesign in the Presence of External Disturbances

    Notes

    Distributed Tracking of Linear Multi-Agent Systems with a Leader of Possibly Nonzero Input

    Problem Statement

    Distributed Discontinuous Tracking Controllers

    Discontinuous Static Controllers

    Discontinuous Adaptive Controllers

    Distributed Continuous Tracking Controllers

    Continuous Static Controllers

    Adaptive Continuous Controllers

    Distributed Output-Feedback Controllers

    Simulation Examples

    Notes

    Containment Control of Linear Multi-Agent Systems with Multiple Leaders

    Containment of Continuous-Time Multi-Agent Systems with Leaders of Zero Inputs

    Dynamic Containment Controllers

    Static Containment Controllers

    Containment Control of Discrete-Time Multi-Agent Systems with Leaders of Zero Inputs

    Dynamic Containment Controllers

    Static Containment Controllers

    Simulation Examples

    Containment of Continuous-Time Multi-Agent Systems with Leaders of Nonzero Inputs

    Distributed Continuous Static Controllers

    Adaptive Continuous Containment Controllers

    Simulation Examples

    Notes

    Distributed Robust Cooperative Control for Multi-Agent Systems with Heterogeneous Matching Uncertainties

    Distributed Robust Leaderless Consensus

    Distributed Static Consensus Protocols

    Distributed Adaptive Consensus Protocols

    Distributed Robust Consensus with a Leader of Nonzero Control Input

    Robustness with Respect to Bounded Non-Matching Disturbances

    Distributed Robust Containment Control with Multiple Leaders

    Notes

    Global Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics

    Global Consensus of Nominal Lipschitz Nonlinear Multi-Agent Systems

    Global Consensus without Disturbances

    Global H1 Consensus Subject to External Disturbances

    Extensions to Leader-Follower Graphs

    Simulation Example

    Robust Consensus of Lipschitz Nonlinear Multi-Agent Systems with Matching Uncertainties

    Distributed Static Consensus Protocols

    Distributed Adaptive Consensus Protocols

    Adaptive Protocols for the Case without Uncertainties

    Simulation Examples

    Notes

    Bibliography

    Index

    Biography

    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.

    "... 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. It’s useful as a reference text and it has a good bibliography."
    Control Technology Consortium (ACTC) E-News, May 2015 Edition