Feedback error learning neural network for stable control of nonlinear nonaffine systems

Abstract

This study presents a stable feedback error learning (FEL) scheme for nonlinear nonaffine systems in the presence of uncertainty and disturbances. The distinguishing feature of the FEL method, which can have a significant effect on both transient and steady-state performance, has led us to adopt this approach. The nonlinear system studied here is nonaffine. In other words, the function that describes the dynamic equations of the system is an implicit function of the control input rather than a particular class of systems. We aim to develop a stable FEL control system with three components: a neural network (NN), a linear controller, and a robustifying control term. To this end, all the adaptation laws for the NN weights are derived from a Lyapunov function, ensuring that the closed-loop system is uniformly asymptotically stable (UAS). Thus, an NN learning control approach that effectively improves the transient performance, as well as the steady-state performance, is proposed, and its remarkable effectiveness is illustrated in comparison with the existing methods.