Abstract
This chapter proposes a convergence analysis of ILC for discrete-time linear systems with randomly iteration-varying lengths. No prior information is required on the probability distribution of randomly iteration-varying lengths. The conventional P-type update law is adopted with Arimoto-like gains and causal gains. The convergence both in almost sure and mean square senses is proved by direct mathematical calculations.
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References
Schmid R (2007) Comments on “Robust optimal design and convergence properties analysis of iterative learning control approaches” and “On the P-type and Newton-type ILC schemes for dynamic systems with non-affine input factors”. Automatica 43(9):1666–1669
Shen D, Zhang W, Wang Y, Chien C-J (2016) On almost sure and mean square convergence of P-type ilc under randomly varying iteration lengths. Automatica 63(1):359–365
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Shen, D., Li, X. (2019). Switching System Techniques for Linear Discrete-Time Systems. In: Iterative Learning Control for Systems with Iteration-Varying Trial Lengths. Springer, Singapore. https://doi.org/10.1007/978-981-13-6136-4_5
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DOI: https://doi.org/10.1007/978-981-13-6136-4_5
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-6135-7
Online ISBN: 978-981-13-6136-4
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