ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEARLY PARAMETERIZED SYSTEMS USING MINIMAL LEARNING PARAMETERS ALGORITHM

Abstract

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-input<br />single-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearly<br />parameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive fuzzy backstepping control scheme<br /> is developed. The main advantages of our approach include: (i) unlike the existing results which deal with the nonlinearly<br />parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the online computation burden greatly, and our development is able to eliminate the problem of ''explosion of complexity" inherent in the existing backstepping-based methods. It is proven that<br />the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, two examples are used to show the effectiveness of the proposed approach.