On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths

Abstract

In this paper, a new class of stochastic impulsive differential equations involving Bernoulli distribution is introduced. For tracking the random discontinuous trajectory, a modified tracking error associated with a piecewise continuous variable by zero-order holder is defined. In the sequel, a new random ILC scheme by adopting global and local iteration average operators is designed too. Sufficient conditions to guarantee the convergence of modified tracking error are obtained by using the tools of mathematical analysis via an impulsive Gronwall inequality. Finally, two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ILC scheme to track the random discontinuous trajectory.