Data-driven tracking control for discrete-time nonlinear systems: a backward difference iterative learning approach

This article investigates the trajectory tracking problem of repeatable discrete-time nonlinear systems with unknown dynamics. The conventional paradigm in this field is to construct an iterative learning controller with the approximately identified model, considering only tracking error information at the current iteration. This leads to the neglect of the error variation trend along historical iterations. To circumvent unmodeled dynamics and capitalise on multi-step iteration error information, a backward difference iterative learning control (BD-ILC) approach is formulated. Initially, a vector data transfer mechanism employing the backward difference iteration error is introduced based on the dynamic data mapping. Within this mechanism, the proportional, differential and quadratic differential control terms are firstly incorporated simultaneously along the iteration domain. Furthermore, a convergence analysis approach is developed using the error deflation spanning tree technique. Simulations validate the enhanced efficacy of the BD-ILC approach, surpassing that of distinct control approaches.