Iterative Learning Control for Multi-agent Systems Coordination

Preface ix 1 Introduction 1 1.1 Introduction to Iterative Learning Control 1 1.1.1 Contraction-Mapping Approach 3 1.1.2 Composite Energy Function Approach 4 1.2 Introduction to MAS Coordination 5 1.3 Motivation and Overview 7 1.4 Common Notations in This Book 9 2 Optimal Iterative Learning Control for Multi-agent Consensus Tracking 11 2.1 Introduction 11 2.2 Preliminaries and Problem Description 12 2.2.1 Preliminaries 12 2.2.2 Problem Description 13 2.3 Main Results 15 2.3.1 Controller Design for Homogeneous Agents 15 2.3.2 Controller Design for Heterogeneous Agents 20 2.4 Optimal Learning Gain Design 21 2.5 Illustrative Example 23 2.6 Conclusion 26 3 Iterative Learning Control for Multi-agent Coordination Under Iteration-Varying Graph 27 3.1 Introduction 27 3.2 Problem Description 28 3.3 Main Results 29 3.3.1 Fixed Strongly Connected Graph 29 3.3.2 Iteration-Varying Strongly Connected Graph 32 3.3.3 Uniformly Strongly Connected Graph 37 3.4 Illustrative Example 38 3.5 Conclusion 40 4 Iterative Learning Control for Multi-agent Coordination with Initial State Error 41 4.1 Introduction 41 4.2 Problem Description 42 4.3 Main Results 43 4.3.1 Distributed D-type Updating Rule 43 4.3.2 Distributed PD-type Updating Rule 48 4.4 Illustrative Examples 49 4.5 Conclusion 50 5 Multi-agent Consensus Tracking with Input Sharing by Iterative Learning Control 53 5.1 Introduction 53 5.2 Problem Formulation 54 5.3 Controller Design and Convergence Analysis 54 5.3.1 Controller Design Without Leader s Input Sharing 55 5.3.2 Optimal Design Without Leader s Input Sharing 58 5.3.3 Controller Design with Leader s Input Sharing 59 5.4 Extension to Iteration-Varying Graph 60 5.4.1 Iteration-Varying Graph with Spanning Trees 60 5.4.2 Iteration-Varying Strongly Connected Graph 60 5.4.3 Uniformly Strongly Connected Graph 62 5.5 Illustrative Examples 63 5.5.1 Example 1: Iteration-Invariant Communication Graph 63 5.5.2 Example 2: Iteration-Varying Communication Graph 64 5.5.3 Example 3: Uniformly Strongly Connected Graph 66 5.6 Conclusion 68 6 A HOIM-Based Iterative Learning Control Scheme for Multi-agent Formation 69 6.1 Introduction 69 6.2 Kinematic Model Formulation 70 6.3 HOIM-Based ILC for Multi-agent Formation 71 6.3.1 Control Law for Agent 1 72 6.3.2 Control Law for Agent 2 74 6.3.3 Control Law for Agent 3 75 6.3.4 Switching Between Two Structures 78 6.4 Illustrative Example 78 6.5 Conclusion 80 7 P-type Iterative Learning for Non-parameterized Systems with Uncertain Local Lipschitz Terms 81 7.1 Introduction 81 7.2 Motivation and Problem Description 82 7.2.1 Motivation 82 7.2.2 Problem Description 83 7.3 Convergence Properties with Lyapunov Stability Conditions 84 7.3.1 Preliminary Results 84 7.3.2 Lyapunov Stable Systems 86 7.3.3 Systems with Stable Local Lipschitz Terms but Unstable Global Lipschitz Factors 90 7.4 Convergence Properties in the Presence of Bounding Conditions 92 7.4.1 Systems with Bounded Drift Term 92 7.4.2 Systems with Bounded Control Input 94 7.5 Application of P-type Rule in MAS with Local Lipschitz Uncertainties 97 7.6 Conclusion 99 8 Synchronization for Nonlinear Multi-agent Systems by Adaptive Iterative Learning Control 101 8.1 Introduction 101 8.2 Preliminaries and Problem Description 102 8.2.1 Preliminaries 102 8.2.2 Problem Description for First-Order Systems 102 8.3 Controller Design for First-Order Multi-agent Systems 105 8.3.1 Main Results 105 8.3.2 Extension to Alignment Condition 107 8.4 Extension to High-Order Systems 108 8.5 Illustrative Example 113 8.5.1 First-Order Agents 114 8.5.2 High-Order Agents 115 8.6 Conclusion 118 9 Distributed Adaptive Iterative Learning Control for Nonlinear Multi-agent Systems with State Constraints 123 9.1 Introduction 123 9.2 Problem Formulation 124 9.3 Main Results 127 9.3.1 Original Algorithms 127 9.3.2 Projection Based Algorithms 135 9.3.3 Smooth Function Based Algorithms 138 9.3.4 Alternative Smooth Function Based Algorithms 141 9.3.5 Practical Dead-Zone Based Algorithms 156 9.4 Illustrative Example 163 9.5 Conclusion 171 10 Synchronization for Networked Lagrangian Systems under Directed Graphs 173 10.1 Introduction 173 10.2 Problem Description 174 10.3 Controller Design and Performance Analysis 175 10.4 Extension to Alignment Condition 181 10.5 Illustrative Example 182 10.6 Conclusion 186 11 Generalized Iterative Learning for Economic Dispatch Problem in a Smart Grid 187 11.1 Introduction 187 11.2 Preliminaries 188 11.2.1 In-Neighbor and Out-Neighbor 188 11.2.2 Discrete-Time Consensus Algorithm 189 11.2.3 Analytic Solution to EDP with Loss Calculation 190 11.3 Main Results 191 11.3.1 Upper Level: Estimating the Power Loss 192 11.3.2 Lower Level: Solving Economic Dispatch Distributively 192 11.3.3 Generalization to the Constrained Case 195 11.4 Learning Gain Design 196 11.5 Application Examples 198 11.5.1 Case Study 1: Convergence Test 199 11.5.2 Case Study 2: Robustness of Command Node Connections 200 11.5.3 Case Study 3: Plug and Play Test 201 11.5.4 Case Study 4: Time-Varying Demand 203 11.5.5 Case Study 5: Application in Large Networks 205 11.5.6 Case Study 6: Relation Between Convergence Speed and Learning Gain 205 11.6 Conclusion 206 12 Summary and Future Research Directions 207 12.1 Summary 207 12.2 Future Research Directions 208 12.2.1 Open Issues in MAS Control 208 12.2.2 Applications 212 Appendix A Graph Theory Revisit 221 Appendix B Detailed Proofs 223 B.1 HOIM Constraints Derivation 223 B.2 Proof of Proposition 2.1 224 B.3 Proof of Lemma 2.1 225 B.4 Proof of Theorem 8.1 227 B.5 Proof of Corollary 8.1 228 Bibliography 231 Index 000