On almost sure and mean square convergence of P-type ILC under randomly varying iteration lengths

This note proposes convergence analysis of iterative learning control (ILC) for discrete-time linear systems with randomly varying iteration lengths. No prior information is required on the probability distribution of randomly varying iteration lengths. The conventional P-type update law is adopted with Arimoto-like gain and/or causal gain. The convergence both in almost sure and mean square senses is proved by direct math calculating. Numerical simulations verifies the theoretical analysis.