Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints

Abstract

This article deals with the design of adaptive fuzzy backstepping control for uncertain nonlinear systems in strict-feedback form with tracking error constraints. In this article, a fuzzy system is used to approximate the unknown nonlinear functions and the differential of virtual control law of each subsystem. In order to satisfy the limitation of tracking error constraints, the barrier Lyapunov function is introduced. Moreover, by applying the minimal learning parameters technique, the number of online parameters update for each subsystem is reduced to only 1. The control scheme not only ensures the tracking error is not to transgress the constraint bounds but also solves the problem of “explosion of complexity” and greatly reduces the initial control input and the number of the adaptive parameters; this provides the conditions for the practical application. The simulation results show the effectiveness of the proposed method.