Prof.
SHEN's Group Distributed Artificial Intelligence Laboratory, ERC-FCDE, MoE School of Mathematics, Renmin University of China |

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Brief Introduction This book presents a comprehensive and detailed study on iterative learning control (ILC) for systems with iteration-varying trial lengths. Instead of traditional ILC, which requires systems to repeat on a fixed time interval, this book focuses on a more practical case where the trial length might randomly vary from iteration to iteration. The iteration-varying trial lengths may be different from the desired trial length, which can cause redundancy or dropouts of control information in ILC, making ILC design a challenging problem. The book focuses on the synthesis and analysis of ILC for both linear and nonlinear systems with iteration-varying trial lengths, and proposes various novel techniques to deal with the precise tracking problem under non-repeatable trial lengths, such as moving window, switching system, and searching-based moving average operator. It not only discusses recent advances in ILC for systems with iteration-varying trial lengths, but also includes numerous intuitive figures to allow reades to develop an in-depth understanding of the intrinsic relationship between the incomplete information environment and the essential tracking performance. This book is intended for academic scholars and engineers who are interested in learning about control, data-driven control, networked control systems, and related fields. It is also a useful resource for graduate students in the above field.. |

Contents

Preface

1 Introduction

Part I Linear Systems

2 Averaging Techniques for Linear Discrete-Time Systems

3 Averaging and Lifting Techniques for Linear Discrete-Time Systems

4 Moving Averaging Techniques for Linear Discrete-Time Systems

5 Switching System Techniques for Linear Discrete-Time Systems

6 Two-Dimensional Techniques for Linear Discrete-Time Systems

Part II Nonlinear Systems

7 Moving Averaging Techniques for Nonlinear Continuous-Time Systems

8 Modified Lambda-Norm Techniques for Nonlinear Discrete-Time Systems

9 Sampled-Data Control for Nonlinear Continuous-Time Systems

10 CEF Techniques for Parameterized Nonlinear Continuous-Time Systems

11 CEF Techniques for Nonparameterized Nonlinear Continuous-Time Systems

12 CEF Techniques for Uncertain Systems with Partial Structure Information

Index

1 Introduction

1.1 Iterative Learning Control

1.2 Basic Formulation of ILC

1.2.1 Discrete-Time Case

1.2.2 Continuous-Time Case

1.3 ILC for Systems with Varying Trial Lengths

1.4 Structure of this Monograph

1.5 Summary

References

1.2 Basic Formulation of ILC

1.2.1 Discrete-Time Case

1.2.2 Continuous-Time Case

1.3 ILC for Systems with Varying Trial Lengths

1.4 Structure of this Monograph

1.5 Summary

References

Part I Linear Systems

2 Averaging Techniques for Linear Discrete-Time Systems

2.1 Problem Formulation

2.2 ILC Design and Convergence Analysis

2.3 Extension to Time-Varying Systems

2.4 Illustrative Simulations

2.5 Summary

References

2.2 ILC Design and Convergence Analysis

2.3 Extension to Time-Varying Systems

2.4 Illustrative Simulations

2.5 Summary

References

3 Averaging and Lifting Techniques for Linear Discrete-Time Systems

3.1 Problem Formulation

3.2 ILC Design and Convergence Analysis

3.3 Extension to Time-Varying Systems

3.4 Illustrative Simulations

3.5 Summary

References

3.2 ILC Design and Convergence Analysis

3.3 Extension to Time-Varying Systems

3.4 Illustrative Simulations

3.5 Summary

References

4 Moving Averaging Techniques for Linear Discrete-Time Systems

4.1 Problem Formulation

4.2 Controller Design I and Convergence Analysis

4.3 Controller Design II and Convergence Analysis

4.4 Illustrative Simulations

4.4.1 Simulations for ILC Law (I)

4.4.2 Simulations for ILC Law (II)

4.5 Summary

References

4.2 Controller Design I and Convergence Analysis

4.3 Controller Design II and Convergence Analysis

4.4 Illustrative Simulations

4.4.1 Simulations for ILC Law (I)

4.4.2 Simulations for ILC Law (II)

4.5 Summary

References

5 Switching System Techniques for Linear Discrete-Time Systems

5.1 Problem Formulation

5.2 ILC Design

5.3 Strong Convergence Properties

5.4 Illustrative Simulations

5.5 Summary

References

5.2 ILC Design

5.3 Strong Convergence Properties

5.4 Illustrative Simulations

5.5 Summary

References

6 Two-Dimensional Techniques for Linear Discrete-Time Systems

6.1 Problem Formulation

6.2 Learning Gain Matrix Design

6.3 Convergence Analysis

6.4 Alternative Scheme with Distribution Estimation

6.5 Illustrative Simulations

6.6 Summary

References

6.2 Learning Gain Matrix Design

6.3 Convergence Analysis

6.4 Alternative Scheme with Distribution Estimation

6.5 Illustrative Simulations

6.6 Summary

References

Part II Nonlinear Systems

7 Moving Averaging Techniques for Nonlinear Continuous-Time Systems

7.1 Problem Formulation

7.2 ILC Design and Convergence Analysis

7.3 Extension to Non-affine Nonlinear Systems

7.4 Illustrative Simulations

7.5 Summary

References

7.2 ILC Design and Convergence Analysis

7.3 Extension to Non-affine Nonlinear Systems

7.4 Illustrative Simulations

7.5 Summary

References

8 Modified Lambda-Norm Techniques for Nonlinear Discrete-Time Systems

8.1 Problem Formulation

8.2 ILC Design

8.3 Convergence Analysis

8.4 Illustrative Simulations

8.5 Summary

References

8.2 ILC Design

8.3 Convergence Analysis

8.4 Illustrative Simulations

8.5 Summary

References

9 Sampled-Data Control for Nonlinear Continuous-Time Systems

9.1 Problem Formulation

9.2 Sampled-Data ILC Design and Convergence Analysis

9.2.1 Generic PD-type ILC Scheme

9.2.2 The Modified ILC Scheme

9.3 Sampled-Data ILC Design with Initial Value Fluctuation

9.3.1 Generic PD-type ILC Scheme

9.3.2 The Modified ILC Scheme

9.4 Illustrative Simulations

9.4.1 Generic PD-type ILC Scheme

9.4.2 The Modified ILC Scheme

9.5 Summary

References

9.2 Sampled-Data ILC Design and Convergence Analysis

9.2.1 Generic PD-type ILC Scheme

9.2.2 The Modified ILC Scheme

9.3 Sampled-Data ILC Design with Initial Value Fluctuation

9.3.1 Generic PD-type ILC Scheme

9.3.2 The Modified ILC Scheme

9.4 Illustrative Simulations

9.4.1 Generic PD-type ILC Scheme

9.4.2 The Modified ILC Scheme

9.5 Summary

References

10 CEF Techniques for Parameterized Nonlinear Continuous-Time Systems

10.1 Problem Formulation

10.2 ILC Algorithm and Its Convergence

10.3 Effect of Random Trial Lengths and Parameters

10.4 Extensions and Discussions

10.4.1 Unknown Lower Bound of the Input Gain

10.4.2 Iteration-Varying Tracking References

10.4.3 High-Order Systems

10.4.4 Multi-input-Multi-output Systems

10.4.5 Parametric Systems with Nonparametric Uncertainty

10.5 Illustrative Simulations

10.6 Summary

References

10.2 ILC Algorithm and Its Convergence

10.3 Effect of Random Trial Lengths and Parameters

10.4 Extensions and Discussions

10.4.1 Unknown Lower Bound of the Input Gain

10.4.2 Iteration-Varying Tracking References

10.4.3 High-Order Systems

10.4.4 Multi-input-Multi-output Systems

10.4.5 Parametric Systems with Nonparametric Uncertainty

10.5 Illustrative Simulations

10.6 Summary

References

11 CEF Techniques for Nonparameterized Nonlinear Continuous-Time Systems

11.1 Problem Formulation

11.2 Robust ILC Algorithms and Their Convergence Analysis

11.2.1 Norm-Bounded Uncertainty Case

11.2.2 Variation-Norm-Bounded Uncertainty Case

11.2.3 Norm-Bounded Uncertainty with Unknown Coefficient Case

11.3 Extension to MIMO System

11.3.1 Norm-Bounded Uncertainty Case

11.3.2 Variation-Norm-Bounded Uncertainty Case

11.4 Illustrative Simulations

11.5 Summary

References

11.2 Robust ILC Algorithms and Their Convergence Analysis

11.2.1 Norm-Bounded Uncertainty Case

11.2.2 Variation-Norm-Bounded Uncertainty Case

11.2.3 Norm-Bounded Uncertainty with Unknown Coefficient Case

11.3 Extension to MIMO System

11.3.1 Norm-Bounded Uncertainty Case

11.3.2 Variation-Norm-Bounded Uncertainty Case

11.4 Illustrative Simulations

11.5 Summary

References

12 CEF Techniques for Uncertain Systems with Partial Structure Information

12.1 Problem Formulation

12.2 Time-Invariant and Time-Varying Mixing Scheme

12.3 Differential-Difference Hybrid Scheme

12.4 Illustrative Simulations

12.5 Summary

References

12.2 Time-Invariant and Time-Varying Mixing Scheme

12.3 Differential-Difference Hybrid Scheme

12.4 Illustrative Simulations

12.5 Summary

References

Index