Iterative Learning Control for Multi-agent Systems Coordination

A timely guide using iterative learning control (ILC) as a solution for multi-agent systems (MAS) challenges, showcasing recent advances and industrially relevant applications

• Explores the synergy between the important topics of iterative learning control (ILC) and multi-agent systems (MAS)

• Concisely summarizes recent advances and significant applications in ILC methods for power grids, sensor networks and control processes

• Covers basic theory, rigorous mathematics as well as engineering practice

Auteur

Shiping Yang, Jian-Xin Xu, and Xuefang Li

National University of Singapore

Dong Shen

Beijing University of Chemical Technology, P.R. China

Contenu

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 Descriptio...