Iterative learning control for distributed parameter systems via Hilfer fractional derivative

This study presents the convergence properties of a Hilfer fractional-order system characterized by distributed parameters. The system under consideration is controlled via a second-order p-type iterative learning control scheme. Our primary focus lies on establishing the stability and convergence of the closed-loop system. To simplify the analysis, the continuous fractional system is initially discretized. Employing the generalized Gronwall inequality, we derive explicit estimates for the tracking error sequence, thereby demonstrating the convergence of the proposed control law. The theoretical results are substantiated through a numerical example, which confirms the validity and effectiveness of the approach. MSC Classification: 34A37; 93C15; 93C40; 93C30; 93C95.