Adaptive fuzzy backstepping control for MIMO uncertain discrete-time nonlinear systems using a set of noisy measurements

Abstract

This paper presents an adaptive fuzzy backstepping control (AFBC) for multi-input and multi-output uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time state equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. The proposed AFBC is simplified in a structure by removing the explosion of complexity problem due to repeated time-differences of nonlinear functions. The modelling errors are approximated by using the fuzzy inference approach based on the extended single input rule modules, and the unknown external disturbances are denoted as unknown time-invariant parameters, and these estimates are derived by using the proposed simplified weighted least squares estimator. It is proved that the errors between the states and the virtual controls, and the estimation errors, are ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.