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Distributed Artificial Intelligence Laboratory, ERC-FCDE, MoE
School of Mathematics, Renmin University of China
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Book:VaryLength
 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
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

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

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

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

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

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

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

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

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

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

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

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

Index

Sample Chapter

Chapter 1: Introduction
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