Robust tracking observer-based adaptive fuzzy control design for uncertain nonlinear MIMO systems with time delayed states

Abstract

This paper addresses the problem of designing robust observer-based adaptive fuzzy tracking control scheme for a class of MIMO nonlinear systems with plant uncertainties, time delayed uncertainties, and external disturbances. A fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions and an adaptive fuzzy observer is introduced for state estimations. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. This allows for the simultaneous inclusion of identifying gains of the delayed state uncertainties and training of the weights of the fuzzy system by introducing estimated error vectors. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with online update laws. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion and the Riccati-inequality to resolve system uncertainties, time delayed uncertainties, and external disturbances. This is done in such a way that all states of the system are bounded and the H∞ tracking performance is achieved. Finally, a two-connected inverted pendulums on carts system (Liu et al., 2011) [29] is used for simulation purposes and some comparisons are given to illustrate the validity and effectiveness of the proposed method.