Analysis of convergence in ILC for nonlinear pantograph equations with impulses using Hilfer fractional derivative

Abstract

 This study aims to formulate a proportional-type iterative learning control (ILC) strategy that incorporates initial state learning for nonlinear pantograph equations with impulsive effects, modeled using Hilfer fractional derivatives. The objective is to achieve accurate tracking of a desired discontinuous output trajectory. To establish robust performance criteria for both open-loop and closed-loop ILC systems, we employ the ($1-\vartheta, \Lambda$)-weighted norm $||\cdot||_{1-\vartheta, \Lambda}$. A detailed illustrative example is presented to validate the theoretical results and highlight their practical applicability.