Iterative learning control for noninstantaneous impulsive fractional-order systems with varying trial lengths

In this paper, we propose five iterative learning control (ILC) schemes for noninstantaneous impulsive fractional-order systems with randomly varying trial lengths. We introduce a domain alignment operator to establish a rigorous convergence analysis for nonlinear fractional-order systems. This operator guarantees that the input, state, output, and tracking error are constrained in a function space that is designed in advance. Moreover, with the help of this operator, we extend the conventional ILC scheme from discrete systems to continuous and algebraic systems with incorporating redundant tracking information. In addition, nonlinear ILC schemes are also presented with a geometric analysis concept. All proposed schemes are shown to be convergent to the desired tracking trajectory. Two illustrative examples are provided to verify the theoretical results.