Iterative learning based convergence analysis for nonlinear impulsive differential inclusion systems with randomly varying trial lengths

This paper studies the finite-time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set-valued mapping in the differential inclusion systems to single-valued mapping by a Steiner-type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero-order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and $\lambda$-norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors.