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Cooperative Control of Multi-Agent Systems A Consensus Region Ap....pdf

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    Front Cover
    Contents
    Preface
    1. Introduction and Mathematical Background
    2. Consensus Control of Linear Multi-Agent Systems: Continuous-Time Case
    3. Consensus Control of Linear Multi-Agent Systems: Discrete-Time Case
    4. H∞ and H2 Consensus Control of Linear Multi-Agent Systems
    5. Consensus Control of Linear Multi-Agent Systems Using Distributed Adaptive Protocols
    6. Distributed Tracking of Linear Multi-Agent Systems with a Leader of Possibly Nonzero Input
    7. Containment Control of Linear Multi-Agent Systems with Multiple Leaders
    8. Distributed Robust Cooperative Control for Multi-Agent Systems with Heterogeneous Matching Uncertainties
    9. Global Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics
    Bibliography
    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 Zhisheng Duan Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business K16462_FM.indd 1 9/17/14 10:01 AM
    AUTOMATION AND CONTROL ENGINEERING A Series of Reference Books and Textbooks Series Editors FRANK L. LEWIS, Ph.D., Fellow IEEE, Fellow IFAC Professor SHUZHI SAM GE, Ph.D., Fellow IEEE Professor The Univeristy of Texas Research Institute The University of Texas at Arlington Interactive Digital Media Institute The National University of Singapore PUBLISHED TITLES Cooperative Control of Multi-agent Systems: A Consensus Region Approach, Zhongkui Li; Zhisheng Duan Nonlinear Control of Dynamic Networks, Tengfei Liu; Zhong-Ping Jiang; David J. Hill Modeling and Control for Micro/Nano Devices and Systems, Ning Xi; Mingjun Zhang; Guangyong Li Linear Control System Analysis and Design with MATLAB®, Sixth Edition, Constantine H. Houpis; Stuart N. Sheldon Real-Time Rendering: Computer Graphics with Control Engineering, Gabriyel Wong; Jianliang Wang Anti-Disturbance Control for Systems with Multiple Disturbances, Lei Guo; Songyin Cao Tensor Product Model Transformation in Polytopic Model-Based Control, Péter Baranyi; Yeung Yam; Péter Várlaki Fundamentals in Modeling and Control of Mobile Manipulators, Zhijun Li; Shuzhi Sam Ge Optimal and Robust Scheduling for Networked Control Systems, Stefano Longo; Tingli Su; Guido Herrmann; Phil Barber Advances in Missile Guidance, Control, and Estimation, S.N. Balakrishna; Antonios Tsourdos; B.A. White End to End Adaptive Congestion Control in TCP/IP Networks, Christos N. Houmkozlis; George A Rovithakis Robot Manipulator Control: Theory and Practice, Frank L. Lewis; Darren M Dawson; Chaouki T. Abdallah Quantitative Process Control Theory, Weidong Zhang Classical Feedback Control: With MATLAB® and Simulink®, Second Edition, Boris Lurie; Paul Enright 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, Guang-Hong Yang; Dan Ye K16462_FM.indd 2 9/17/14 10:01 AM
    Reinforcement Learning and Dynamic Programming Using Function Approximators, Lucian Busoniu; Robert Babuska; Bart De Schutter; Damien Ernst Modeling and Control of Vibration in Mechanical Systems, Chunling Du; Lihua Xie 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, Vadim Utkin; Juergen Guldner; Jingxin Shi Autonomous Mobile Robots: Sensing, Control, Decision Making and Applications, Shuzhi Sam Ge; Frank L. Lewis Linear Control Theory: Structure, Robustness, and Optimization, Shankar P. Bhattacharyya; Aniruddha Datta; Lee H.Keel Optimal Control: Weakly Coupled Systems and Applications, Zoran Gajic Deterministic Learning Theory for Identification, Recognition, and Control, Cong Wang; David J. Hill Intelligent Systems: Modeling, Optimization, and Control, Yung C. Shin; Myo-Taeg Lim; Dobrila Skataric; Wu-Chung Su; Vojislav Kecman FORTHCOMING TITLES Modeling and Control Dynamic Sensor Network, Silvia Ferrari; Rafael Fierro; Thomas A. Wettergren Optimal Networked Control Systems, Jagannathan Sarangapani; Hao Xu K16462_FM.indd 3 9/17/14 10:01 AM
    MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® soft- ware or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140916 International Standard Book Number-13: 978-1-4665-6997-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
    Contents Preface 1 Introduction and Mathematical Background 1.1 Introduction to Cooperative Control of Multi-Agent Systems 1.1.1 Consensus . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Formation Control . . . . . . . . . . . . . . . . . . . . 1.1.3 Flocking . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Overview of This Monograph . . . . . . . . . . . . . . . . . . 1.3 Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . 1.3.1 Notations and Definitions . . . . . . . . . . . . . . . . 1.3.2 Basic Algebraic Graph Theory . . . . . . . . . . . . . 1.3.3 Stability Theory and Technical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Notes vii 1 1 4 6 7 7 9 9 11 16 18 2 Consensus Control of Linear Multi-Agent Systems: Continuous- Time Case 2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 2.2 State Feedback Consensus Protocols . . . . . . . . . . . . . . 2.2.1 Consensus Condition and Consensus Value . . . . . . 2.2.2 Consensus Region . . . . . . . . . . . . . . . . . . . . 2.2.3 Consensus Protocol Design . . . . . . . . . . . . . . . 19 20 21 22 24 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Full-Order Observer-Type Protocol I . . . . . . . . . . 2.3.2 Full-Order Observer-Type Protocol II . . . . . . . . . 2.3.3 Reduced-Order Observer-Based Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Observer-Type Consensus Protocols 33 35 35 40 41 43 45 50 2.4 Extensions to Switching Communication Graphs 2.5 Extension to Formation Control 2.6 Notes 3 Consensus Control of Linear Multi-Agent Systems: Discrete- Time Case 3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 53 54 v
    vi Contents 3.2 State Feedback Consensus Protocols . . . . . . . . . . . . . . 3.2.1 Consensus Condition . . . . . . . . . . . . . . . . . . . 3.2.2 Discrete-Time Consensus Region . . . . . . . . . . . . 3.2.3 Consensus Protocol Design . . . . . . . . . . . . . . . 54 55 57 59 3.2.3.1 The Special Case with Neutrally Stable Agents 60 62 3.2.3.2 The General Case . . . . . . . . . . . . . . . 65 . . . . . . . . . . . . . . 3.3.1 Full-Order Observer-Type Protocol I . . . . . . . . . . 65 67 3.3.2 Full-Order Observer-Type Protocol II . . . . . . . . . 68 3.3.3 Reduced-Order Observer-Based Protocol . . . . . . . . 69 . . . . . . . . . . . . . . . 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4 Application to Formation Control 3.5 Discussions 3.6 Notes 3.3 Observer-Type Consensus Protocols 4 H∞ and H2 Consensus Control of Linear Multi-Agent Sys- tems 4.1 H∞ Consensus on Undirected Graphs . . . . . . . . . . . . . 4.1.1 Problem Formulation and Consensus Condition . . . . 4.1.2 H∞ Consensus Region . . . . . . . . . . . . . . . . . . 4.1.3 H∞ Performance Limit and Protocol Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Leader-Follower Graphs . . . . . . . . . . . . . . . . . Strongly Connected Directed Graphs . . . . . . . . . . 4.3.2 4.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 H2 Consensus on Undirected Graphs 4.3 H∞ Consensus on Directed Graphs 5 Consensus Control of Linear Multi-Agent Systems Using Dis- tributed Adaptive Protocols 5.1 Distributed Relative-State Adaptive Consensus Protocols . . 5.1.1 Consensus Using Edge-Based Adaptive Protocols . . . 5.1.2 Consensus Using Node-Based Adaptive Protocols . . . 5.1.3 Extensions to Switching Communication Graphs . . . 5.2 Distributed Relative-Output Adaptive Consensus Protocols . 5.2.1 Consensus Using Edge-Based Adaptive Protocols . . . 5.2.2 Consensus Using Node-Based Adaptive Protocols . . . 5.2.3 Simulation Examples . . . . . . . . . . . . . . . . . . . 5.3 Extensions to Leader-Follower Graphs . . . . . . . . . . . . . 5.4 Robust Redesign of Distributed Adaptive Protocols . . . . . 5.4.1 Robust Edge-Based Adaptive Protocols . . . . . . . . 5.4.2 Robust Node-Based Adaptive Protocols . . . . . . . . 5.4.3 Simulation Examples . . . . . . . . . . . . . . . . . . . 5.5 Distributed Adaptive Protocols for Graphs Containing Direct- ed Spanning Trees . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Distributed Adaptive Consensus Protocols . . . . . . . 73 74 74 77 80 83 85 85 87 92 93 95 96 100 101 103 104 107 109 111 114 115 119 121 123 123
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