Iterative Learning Control for Hilfer‐Type Fractional Stochastic Differential Systems: A Simulation Study for Robotic Applications

Abstract

ABSTRACT This paper investigates iterative learning control for stochastic differential systems of fractional order in the Hilfer sense. Unlike existing studies that treat either fractional dynamics or stochastic effects separately, we develop an integrated framework that combines Hilfer fractional derivatives, Brownian perturbations, and a proportional–fractional integral learning law. The proposed approach captures both the memory effects and random uncertainties inherent in complex systems. As a case study, we apply the method to a gantry robot equipped with a flexible arm. Numerical simulations show that the Hilfer derivative significantly improves tracking accuracy and convergence speed compared to integer‐order models, highlighting the potential of the proposed strategy for robotic applications under uncertainty.