Simple Adaptive Asymptotic Tracking Scheme for Parametric Strict-Feedback Nonlinear Systems with Additive Disturbance

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1. Introduction

Disturbance can be encountered in many physical systems. The control problem of such systems has received much attention in the past decades. For example, in [1], a class of single-input-single-out linear systems with unmodelled dynamics and input and output disturbances were considered. A dynamic normalizing signal and a smooth switching-σ function were introduced to design adaptive backstepping controller, and the mean-squared tracking error bound was established. In [2], adaptive control of the perturbed nonlinear output feedback systems was investigated. The Lyapunov functions with flat zone were employed, and the flat-zone modifications were incorporated into the intermediate control functions. The output error was proved to converge to arbitrary small interval around zero. However, in most of control literature, asymptotic regulation or tracking could not be achieved, and the system stability was established only in the sense that all the closed-loop signals were bounded (see, e.g., [1–25]).

Recently, Cai et al. proposed a new class of adaptive controllers to deal with the control problem of nonlinear systems with disturbance [26–28]. Two special cases were firstly reported in the control conferences (see [26, 27]). In [26], the tracking problem for nonlinear parametric strict-feedback systems of relative degree two in the presence of matched additive disturbance were studied. In [27], the regulation problem for n th-order nonlinear systems in the strict-feedback form was addressed. Then, in a more general case, the tracking control of strict-feedback n th-order nonlinear systems with parametric uncertainties and additive disturbance was considered. The main contributions of these works were that continuous adaptive controllers were designed and asymptotic tracking performance was ensured. The...