Prof.
Dong
SHEN's Group Center of Intelligent and Learning Systems School of Mathematics, Renmin University of China |

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Brief Introduction The primary objective of this monograph is to present a systematic framework of ILC algorithms design and analysis for stochastic systems with passive incomplete information. By passive incomplete information we mean the incomplete operation information and data caused by the system and transmission limitations during data collecting, storing, transmitting, and processing stages. For example, when applying ILC to practical systems, the operation may end early in consideration of safety when the system output largely deviates from the desired operation zone, which yields an incomplete iteration. For another example, when transmitting the data through wireless networks, the communication channel may suffer data dropouts, communication delays, fading, and data disordering, which surely degrades the data quality and induces incomplete information. In addition, limited transmission bandwidth and memory capacity will apparently exclude part data as we cannot accommodate all the information, whence only incomplete information is available for learning update. In consideration of all the mentioned passive incomplete information problems, we have established a unified framework for the design and analysis of ILC schemes based on stochastic approximation theory in this monograph. Indeed, the stochastic approximation is a quite effective tool for solving the stochastic control and optimization problems, which inspires us to consider the application of stochastic approximation in dealing with stochastic ILC problems under various incomplete information environments. We anticipate that the techniques provided in this monograph can help to solve more networked ILC problems. |

Contents

Preface

1 Introduction

Part I One-Side Data Dropout

2 Random Sequence Model for Linear Systems

3 Random Sequence Model for Nonlinear Systems

4 Random Sequence Model for Nonlinear Systems with Unknown Control Direction

5 Bernoulli Variable Model for Linear Systems

6 Bernoulli Variable Model for Nonlinear Systems

7 Markov Chain Model for Linear Systems

Part II Two-Side Data Dropout

8 Two-Side Data Dropout for Linear Deterministic Systems

9 Two-Side Data Dropout for Linear Stochastic Systems

10 Two-Side Data Dropout for Nonlinear Systems

Part III General Incomplete Information Conditions

11 Multiple Communication Conditions and Finite Memory

12 Random Iteration-Varying Lengths for Linear Systems

13 Random Iteration-Varying Lengths for Nonlinear Systems

14 Iterative Learning Control for Large-Scale Systems

Appendix

Index

1 Introduction

1.1 Iterative Learning Control—Why and
How

1.2 Basic Formulation of ILC

1.2.1 Discrete-Time Case

1.2.2 Continuous-Time Case

1.3 ILC with Random Data Dropouts

1.3.1 Data Dropout Models

1.3.2 Data Dropout Positions

1.3.3 Convergence Meanings

1.4 ILC with Other Incomplete Information

1.4.1 Communication Delay and Asynchronism

1.4.2 Iteration-Varying Lengths

1.5 Structure of This Monograph

1.6 Summary

References

1.2 Basic Formulation of ILC

1.2.1 Discrete-Time Case

1.2.2 Continuous-Time Case

1.3 ILC with Random Data Dropouts

1.3.1 Data Dropout Models

1.3.2 Data Dropout Positions

1.3.3 Convergence Meanings

1.4 ILC with Other Incomplete Information

1.4.1 Communication Delay and Asynchronism

1.4.2 Iteration-Varying Lengths

1.5 Structure of This Monograph

1.6 Summary

References

Part I One-Side Data Dropout

2 Random Sequence Model for Linear Systems

2.1 Problem Formulation

2.2 Intermittent Update Scheme and Its Almost Sure Convergence

2.3 Extension to Arbitrary Relative Degree Case with Mean Square Convergence

2.3.1 Noise-Free System Case

2.3.2 Stochastic System Case

2.4 Illustrative Simulations

2.5 Summary

References

2.2 Intermittent Update Scheme and Its Almost Sure Convergence

2.3 Extension to Arbitrary Relative Degree Case with Mean Square Convergence

2.3.1 Noise-Free System Case

2.3.2 Stochastic System Case

2.4 Illustrative Simulations

2.5 Summary

References

3 Random Sequence Model for Nonlinear Systems

3.1 Problem Formulation

3.2 Intermittent Update Scheme and Its Convergence

3.3 Successive Update Scheme and Its Convergence

3.4 Illustrative Simulations

3.5 Summary

References

3.2 Intermittent Update Scheme and Its Convergence

3.3 Successive Update Scheme and Its Convergence

3.4 Illustrative Simulations

3.5 Summary

References

4 Random Sequence Model for Nonlinear Systems with Unknown Control Direction

4.1 Problem Formulation

4.2 Intermittent Update Scheme and Its Almost Sure Convergence

4.3 Proofs of Lemmas

4.4 Illustrative Simulations

4.5 Summary

References

4.2 Intermittent Update Scheme and Its Almost Sure Convergence

4.3 Proofs of Lemmas

4.4 Illustrative Simulations

4.5 Summary

References

5 Bernoulli Variable Model for Linear Systems

5.1 Problem Formulation

5.2 Intermittent Update Scheme and Its Almost Sure Convergence

5.3 Successive Update Scheme and Its Almost Sure Convergence

5.4 Mean Square Convergence of Intermittent Update Scheme

5.4.1 Noise-Free System Case

5.4.2 Stochastic System Case

5.5 Illustrative Simulations

5.5.1 System Description

5.5.2 Tracking Performance of both Schemes

5.5.3 Comparison of Different Data Dropout Rates

5.5.4 Comparison of Different Learning Gains

5.5.5 Comparison with Conventional P-Type Algorithm

5.6 Summary

References

5.2 Intermittent Update Scheme and Its Almost Sure Convergence

5.3 Successive Update Scheme and Its Almost Sure Convergence

5.4 Mean Square Convergence of Intermittent Update Scheme

5.4.1 Noise-Free System Case

5.4.2 Stochastic System Case

5.5 Illustrative Simulations

5.5.1 System Description

5.5.2 Tracking Performance of both Schemes

5.5.3 Comparison of Different Data Dropout Rates

5.5.4 Comparison of Different Learning Gains

5.5.5 Comparison with Conventional P-Type Algorithm

5.6 Summary

References

6 Bernoulli Variable Model for Nonlinear Systems

6.1 Problem Formulation

6.2 Intermittent Update Scheme and Its Almost Sure Convergence

6.3 Successive Update Scheme and Its Almost Sure Convergence

6.4 Illustrative Simulations

6.5 Summary

References

6.2 Intermittent Update Scheme and Its Almost Sure Convergence

6.3 Successive Update Scheme and Its Almost Sure Convergence

6.4 Illustrative Simulations

6.5 Summary

References

7 Markov Chain Model for Linear Systems

7.1 Problem Formulation

7.2 ILC Algorithms

7.3 ILC for Classical Markov Chain Model Case

7.4 ILC for General Markov Data Dropout Model Case

7.5 Illustrative Simulations

7.6 Summary

References

7.2 ILC Algorithms

7.3 ILC for Classical Markov Chain Model Case

7.4 ILC for General Markov Data Dropout Model Case

7.5 Illustrative Simulations

7.6 Summary

References

Part II Two-Side Data Dropout

8 Two-Side Data Dropout for Linear Deterministic Systems

8.1 Problem Formulation

8.2 ILC Algorithms

8.3 Markov Chain Model of Input Evolution

8.4 Convergence Analysis

8.5 Illustrative Simulations

8.6 Summary

References

8.2 ILC Algorithms

8.3 Markov Chain Model of Input Evolution

8.4 Convergence Analysis

8.5 Illustrative Simulations

8.6 Summary

References

9 Two-Side Data Dropout for Linear Stochastic Systems

9.1 Problem Formulation

9.2 Markov Chain of Input Evolution

9.3 Convergence Analysis

9.4 Discussions on Convergence Speed

9.5 Illustrative Simulations

9.6 Summary

References

9.2 Markov Chain of Input Evolution

9.3 Convergence Analysis

9.4 Discussions on Convergence Speed

9.5 Illustrative Simulations

9.6 Summary

References

10 Two-Side Data Dropout for Nonlinear Systems

10.1 Problem Formulation

10.2 Convergence Analysis of ILC Algorithms

10.3 Extensions to Non-affine Nonlinear Systems

10.4 Illustrative Simulations

10.5 Summary

References

10.2 Convergence Analysis of ILC Algorithms

10.3 Extensions to Non-affine Nonlinear Systems

10.4 Illustrative Simulations

10.5 Summary

References

Part III General Incomplete Information Conditions

11 Multiple Communication Conditions and Finite Memory

11.1 Problem Formulation

11.2 Communication Constraints

11.3 Control Objective and Preliminary Lemmas

11.4 Intermittent Update Scheme and Its Almost Sure Convergence

11.5 Successive Update Scheme and Its Almost Sure Convergence

11.6 Illustrative Simulations

11.6.1 Intermittent Update Scheme Case

11.6.2 Successive Update Scheme Case

11.6.3 Intermittent Update Scheme Versus Successive Update Scheme

11.7 Proofs of Theorems

11.8 Summary

References

11.2 Communication Constraints

11.3 Control Objective and Preliminary Lemmas

11.4 Intermittent Update Scheme and Its Almost Sure Convergence

11.5 Successive Update Scheme and Its Almost Sure Convergence

11.6 Illustrative Simulations

11.6.1 Intermittent Update Scheme Case

11.6.2 Successive Update Scheme Case

11.6.3 Intermittent Update Scheme Versus Successive Update Scheme

11.7 Proofs of Theorems

11.8 Summary

References

12 Random Iteration-Varying Lengths for Linear Systems

12.1 Problem Formulation

12.2 ILC Design

12.3 Strong Convergence Properties

12.4 Illustrative Simulations

12.5 Summary

References

12.2 ILC Design

12.3 Strong Convergence Properties

12.4 Illustrative Simulations

12.5 Summary

References

13 Random Iteration-Varying Lengths for Nonlinear Systems

13.1 Problem Formulation

13.2 ILC Design

13.3 Convergence Analysis

13.4 Illustrative Simulations

13.5 Summary

References

13.2 ILC Design

13.3 Convergence Analysis

13.4 Illustrative Simulations

13.5 Summary

References

14 Iterative Learning Control for Large-Scale Systems

14.1 Problem Formulation

14.2 Optimal Control

14.3 Optimal ILC Algorithms and Convergence Analysis

14.4 Illustrative Example

14.5 Summary

References

14.2 Optimal Control

14.3 Optimal ILC Algorithms and Convergence Analysis

14.4 Illustrative Example

14.5 Summary

References

Appendix

Index