Title: Simplified algorithm of an adaptive fuzzy backstepping control for MIMO uncertain discrete-time nonlinear systems using a set of noisy measurements
Authors: Toshio Yoshimura
Addresses: The University of Tokushima, Minamijosanjima 2-1, Tokushima 770-8506, Japan
Abstract: This paper presents a simplified algorithm of an adaptive fuzzy backstepping control (AFBC) for multi-input multi-output uncertain discrete-time nonlinear systems with uncertainties viewed as the modelling errors and the unknown external disturbances, and the observation of the states is taken with measurement noises. The simplified algorithm of the proposed AFBC is designed as follows. The explosion of complexity problem due to repeated computation of nonlinear functions is removed to derive the simplified algorithm at the first stage, secondly the number of the adjustable parameters is reduced by using the fuzzy inference approach based on the proposed simplified extended single input rule modules, and finally the simplified weighted least squares estimator is constructed by reducing the computational burden of the estimation for the un-measurable states and the adjustable parameters. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.
Keywords: adaptive fuzzy backstepping control; AFBC; multi-input multi-output uncertain discrete-time nonlinear system; virtual control; fuzzy IF-THEN rules; simplified extended single input rule modules; universal approximation theorem; simplified weighted least squares estimator.
International Journal of Modelling, Identification and Control, 2017 Vol.27 No.3, pp.200 - 209
Received: 19 May 2015
Accepted: 27 Apr 2016
Published online: 22 Apr 2017 *