Tracking Control for Stochastic Learning Systems Over Changing Durations

—How to establish control design methods for learning systems that are subjected to the stochastic uncertainties becomes a topic of practical importance in the control field. This paper deals with the stochastic iterative learning control (ILC) problems for linear time-varying systems subject to measurement noises and changing durations. The lengths of the changing durations are modeled as a Markov chain with finite states. By exploring the essential trackability problem, we develop a trackability-based design and analysis framework for the stochastic ILC systems. Besides, we design three trackability-based P-type stochastic ILC updating laws to achieve the tracking tasks, with some simple gain matrix selection conditions. Further, the convergence results for the stochastic ILC systems in both the almost-sure and mean-square senses are developed. Two illustrative examples are included to demonstrate the effectiveness of the trackability-based stochastic ILC results.