Introduction
Cooperative Control of Nonlinear Networked Systems is concerned with the distributed cooperative control of multiple networked nonlinear systems in the presence of unknown non-parametric uncertainties and non-vanishing disturbances under certain communication conditions. It covers stability analysis tools and distributed control methods for analyzing and synthesizing nonlinear networked systems. The book presents various solutions to cooperative control problems of multiple networked nonlinear systems on graphs.
The book includes various examples with segments of MATLAB® codes for readers to verify, validate, and replicate the results. The authors present a series of new control results for nonlinear networked systems subject to both non-parametric and non-vanishing uncertainties, including the cooperative uniformly ultimately bounded (CUUB) result, finite-time stability result, and finite-time cooperative uniformly ultimately bounded (FT-CUUB) result. With some mathematical tools, such as algebraic graph theory and certain aspects of matrix analysis theory introduced by the authors, the readers can obtain a deeper understanding of the roles of matrix operators as mathematical machinery for cooperative control design for multi-agent systems.
Cooperative Control of Nonlinear Networked Systems is a valuable source of information for researchers and engineers in cooperative adaptive control, as its technical contents are presented with examples in full analytical and numerical detail, and graphically illustrated for easy-to-understand results. Scientists in research institutes and academics in universities working on nonlinear systems, adaptive control and distributed control will find the book of interest, as it contains multi-disciplinary problems and covers different areas of research.
Author(s): Yongduan Song； Yujuan Wang
Series: Communications and Control Engineering
Publisher: Springer
Year: 2019
Language: English
Pages: 206
Tags: Cooperative Control; Nonlinear Networked Systems; Infinite-time and Finite-time Design Methods
Preface......Page 7
Contents......Page 11
Abbreviations and Notation......Page 15
Part I Overview and Preliminary......Page 17
1.1 Cooperative Control of Multi-agent Systems......Page 18
1.2 Overview of Recent Research Results in Cooperative Control of Multi-agent Systems......Page 21
1.2.1 Non-finite Time Convergence......Page 22
1.2.2 Increased Convergence Speed......Page 24
1.2.3 Finite-Time Convergence......Page 25
References......Page 33
2.1 Algebraic Graph Theory......Page 40
2.2 Matrix Analysis on Graphs......Page 41
2.3 Matrix and Algebra Theory Background......Page 43
2.4 Stability Analysis Theory on Cooperative Control Systems......Page 45
References......Page 49
Part II Infinite-Time Cooperative Adaptive Control of Multiple Networked Nonlinear Systems......Page 50
3 Lyapunov Analysis for Cooperative Adaptive Consensus Under Undirected Graph......Page 51
3.1 Leaderless Consensus Formulation......Page 52
3.2 Core Function and Virtual Parameter Estimation Error......Page 53
3.3.1 The Distributed Part of Lyapunov Function......Page 56
3.4 Lyapunov Analysis for Adaptive Leaderless Consensus......Page 58
References......Page 61
4 Cooperative Adaptive Consensus Control for Uncertain Multi-agent Systems with nth-Order Dynamics Under Undirected Graph......Page 62
4.1.1 System Dynamics......Page 63
4.1.2 Controller Design and Stability Analysis......Page 64
4.1.3 Simulation Example......Page 68
4.2 Second-Order Systems......Page 70
4.2.2 Controller Design and Stability Analysis......Page 71
4.2.3 Simulation Example......Page 75
4.3.1 Consensus Error Dynamics......Page 78
4.3.2 Controller Design and Stability Analysis......Page 79
4.4 Discussion on Cooperative Adaptive Consensus of MAS with Non-parametric Uncertainties......Page 82
References......Page 83
5 Cooperative Adaptive Consensus for Multi-agent Systems Under Directed Topology......Page 85
5.1 Graph Laplacian Potential Under Directed Topology......Page 86
5.2.1 Problem Formulation......Page 89
5.2.2 Controller Design and Stability Analysis for First-Order Systems......Page 90
5.3 Leaderless Consensus of Second-Order Uncertain Systems Under Directed Topology......Page 91
5.3.1 Problem Formulation—Second-Order Uncertain Systems Under Directed Topology......Page 92
5.3.2 Leaderless Consensus Control Design and Stability Analysis......Page 93
5.4 Simulation Examples......Page 102
References......Page 106
Part III Finite-Time Cooperative Adaptive Control for Multiple Networked Nonlinear Systems......Page 107
6 Finite-Time Leaderless Consensus Control for Systems with First-Order Uncertain Dynamics......Page 108
6.1 Preliminaries for the Finite-Time Control......Page 109
6.2 Finite-Time Leaderless Consensus Control Under Undirected Topology......Page 110
6.2.1 Problem Formulation of Finite-Time Leaderless Consensus for First-Order Uncertain Systems......Page 111
6.2.2 Finite-Time Leaderless Consensus Control Design......Page 112
6.2.3 Finite-Time Leaderless Consensus Stability Analysis......Page 113
6.2.4 Comparison with Regular State Feedback-Based Infinite-Time Method......Page 120
6.2.5 Notes......Page 121
6.3.1 Problem Formulation......Page 122
6.3.2 Lyapunov Function Design Under Directed Topology......Page 123
6.3.3 Finite-Time Leaderless Consensus Control Design and Stability Analysis Under Directed Topology......Page 124
6.4 Simulation Example......Page 126
References......Page 129
7 Finite-Time Consensus for Systems with Second-Order Uncertain Dynamics Under Undirected Topology......Page 131
7.1 Formulation of Finite-Time Consensus for Second-Order Uncertain Systems......Page 132
7.2 Useful Lemmas......Page 133
7.3 Distributed Adaptive Finite-Time Control for Second-Order Uncertain Systems......Page 134
7.3.1 Finite-Time Consensus Control Design......Page 135
7.3.2 Finite-Time Consensus Stability Analysis......Page 136
7.4 Numerical Simulations......Page 146
References......Page 152
8 Finite-Time Consensus for Systems with Second-Order Uncertain Dynamics Under Directed Topology......Page 153
8.1.1 Control Problem Formulation Under Directed Topology......Page 154
8.2.1 Useful Lemmas Related to Finite-Time Control......Page 155
8.2.2 Lyapunov Function Design Under Directed Topology......Page 158
8.3 Distributed Adaptive Finite-Time Control Design and Stability Analysis Under Directed Topology......Page 159
8.3.1 Comparison with Regular State Feedback-Based Infinite-Time Method Under Directed Topology......Page 170
8.4 Numerical Simulations......Page 171
8.5 Notes......Page 177
References......Page 178
9 Finite-Time Leaderless Consensus Control for Systems with High-Order Uncertain Dynamics......Page 180
9.1 Finite-Time Consensus Formulation for High-Order Uncertain Systems......Page 181
9.2 Useful Lemmas and Intermediate Results......Page 182
9.3 Inductive Controller Design......Page 186
9.4 The Finite-Time Stability Analysis for the Uncertain High-Order MAS......Page 194
9.5 Comparison with Regular State Feedback-Based Infinite-Time Method......Page 198
9.6 Numerical Simulations......Page 200
9.7 Notes......Page 202
References......Page 205
