Iterative learning control for two-dimensional linear discrete systems with Fornasini-Marchesini model

Abstract

Almost all existing iterative learning control (ILC) algorithms have focused on one-dimensional (1-D) dynamical systems, and seldom were designed for multidimensional systems. In this article, a two-gain ILC law is presented to deal with the ILC issue of two-dimensional (2-D) linear discrete systems described by the first Fornasini-Marchesini model (FMMI). Convergence and robustness of the proposed ILC law under two different cases of boundary conditions are discussed, respectively. A super-vector technique is used to transfer the ILC process of 2-D FMMI into a 2-D Roessor model such that sufficient convergence/robustness conditions of the proposed ILC law are derived. An illustrative example is given to validate the effectiveness of the proposed ILC approach.