Forgetting Factor Nonlinear Functional Analysis for Iterative Learning System with Time-Varying Disturbances and Unknown Uncertain

Abstract

This paper focuses on the iterative learning tracking control problem for a class of nonlinear system with time-varying disturbances. First, because of the mismatches in time-varying disturbances functions, a high-order feed-forward iterative learning control (ILC) is employed to change the original system into an iterative system. Secondly, a variable forgetting factor is developed to stabilize the system. Based on the feed-forward iterative learning controller, a memory controller is constructed for the nonlinear system. By choosing a new variable forgetting factor, we show that the designed continuous adaptive controller makes the solutions of the closed-loop system convergent to a ball exponentially. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed method.

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

“…Liu and Wang (2017) proposed a new ILCFF comprising an output equation with nonlinear input to deal with various tracking problems in the finite time intervals of fractional order systems. In Zheng et al (2017), a memory ILC controller with a variable forgetting factor was constructed for a nonlinear system. However, they focused only on algorithm convergence, and an in-depth analysis of the forgetting factor effect on system output characteristics was not performed.…”