Direct adaptive control for a class of discrete-time unknown nonaffine nonlinear systems using neural networks

Abstract

In this paper, a direct adaptive state-feedback control approach is developed for a class of nonlinear systems in discrete-time (DT) domain. We study MIMO unknown nonaffine nonlinear DT systems and employ a two-layer NN to design the controller. By using the presented method, the NN approximation is able to cancel the nonlinearity of the unknown DT plant. Meanwhile, pretraining is not required, and the weights of NNs used in adaptive control are directly updated online. Moreover, unlike standard NN adaptive controllers yielding uniform ultimate boundedness results, the tracking error is guaranteed to be uniformly asymptotically stable by utilizing Lyapunov's direct method. Two illustrative examples are provided to demonstrate the effectiveness and the applicability of the theoretical results.