Adaptive Fuzzy Synchronization for Uncertain Chaotic Systems with Different Dimensions and Disturbances

Abstract

This paper focuses on the design of a novel adaptive fuzzy controller to synchronize the uncertain master-slave chaotic systems with different dimensions. In this paper, completely unknown nonlinear structures and disturbances exist in both the master and slave systems. For such systems, the definition of the generalized linear master-slave synchronization (GLMSS) is proposed. And different from the existing literatures, it is the unknown norm bound function of the uncertain structure to be approximated by the fuzzy logic system. Thus, regardless of the number of the nonlinear functions in the master and slave systems' unknown structures, only two fuzzy logic systems are needed to synthesize the adaptive controller which guarantees the two systems achieving GLMSS. Three numerical examples are given to verify the effectiveness and feasibility of the fuzzy adaptive control scheme in this paper.