Iterative Learning Control for Equations with Fractional Derivatives and Impulses

Description

This book introduces iterative learning control (ILC) and its applications to the new equations such as fractional order equations, impulsive equations, delay equations, and multi-agent systems, which have not been presented in other books on conventional fields. ILC is an important branch of intelligent control, which is applicable to robotics, process control, and biological systems. The fractional version of ILC updating laws and formation control are presented in this book. ILC design for impulsive equations and inclusions are also established. The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique. This book is useful for graduate students studying ILC involving fractional derivatives and impulsive conditions as well as for researchers working in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines. Preface Acknowledgements Contents 1 Introduction 2 Fractional Equations 2.1 Pulse Compensation ILC 2.1.1 Equations and ILC Laws 2.1.2 Convergence Analysis 2.1.3 Example 2.1.4 Conclusion 2.2 PD-Type ILC 2.2.1 Equations and ILC Laws 2.2.2 Convergence Analysis 2.2.3 Example 2.2.4 Conclusion 2.3 High-Order Internal Models ILC 2.3.1 Equations and ILC Laws 2.3.2 Convergence Analysis 2.3.3 Convergence Results for Part I 2.3.4 Convergence Results for Part II 2.3.5 Convergence Results for Part III 2.3.6 Example 2.3.7 Conclusions 2.4 Randomly Varying Trial Lengths ILC 2.4.1 Equations and ILC Laws 2.4.2 Convergence Analysis 2.4.3 Randomly Varying Trial Lengths with Dα-Type Learning Law 2.4.4 Randomly Varying Trial Lengths with PDα-Type Learning Law 2.4.5 Randomly Varying Trial Lengths with P I1-α Dα-Type Learning Law 2.4.6 Randomly Varying Trial Lengths with P Iβ Dα-Type Learning Law 2.4.7 Example 2.4.8 Conclusions 3 Fractional Multi-agent Systems 3.1 Linear Systems 3.1.1 Systems and ILC Laws 3.1.2 Convergence Analysis 3.1.3 Example 3.1.4 Conclusion 3.2 Nonlinear Systems 3.2.1 Systems and ILC Laws 3.2.2 Convergence Analysis 3.2.3 Example 3.2.4 Conclusions 3.2.5 Systems and ILC Laws 3.2.6 Convergency Analysis 3.2.7 Conclusions 4 Instantaneous Impulsive Differential Equations 4.1 ODEs Case 4.1.1 Systems and ILC Laws 4.1.2 Convergence Analysis 4.1.3 Example 4.1.4 Conclusions 4.2 Random Case 4.2.1 System and ILC Laws 4.2.2 Convergence Analysis 4.2.3 Example 4.2.4 Conclusion 4.3 Delay Case 4.3.1 Systems and ILC Laws 4.3.2 Convergence Analysis 4.3.3 Example 4.3.4 Conclusions 5 Noninstantaneous Impulsive Equations 5.1 Fixed Trial Lengths 5.1.1 Equations 5.1.2 Existence and Approximate Controllability Results 5.1.3 Convergence Analysis 5.1.4 Example 5.1.5 Conclusion 5.2 Varying Trial Lengths 5.2.1 Equations and ILC Laws 5.2.2 Convergence Analysis 5.2.3 Examples 5.2.4 Conclusion 6 Nonlinear Differential Inclusion 6.1 Ordinary Differential Inclusion 6.1.1 Systems and ILC Laws 6.1.2 Analysis of Convergence 6.1.3 Examples 6.1.4 Conclusions 6.2 Partial Differential Inclusion 6.2.1 Systems and ILC Laws 6.2.2 Main Result 6.2.3 Examples 6.2.4 Conclusions 7 Conclusion and Expectation Appendix References