Iterative Learning Control for Equations with Fractional Derivatives and Impulses

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