Generalized Projective Chaos Synchronization of Coupled Duffing System by Using Fuzzy Sliding Mode Control

摘要

This paper presents a robust control scheme for generalized synchronization between two identical coupled Duffing systems subject to external disturbances. Owing to the nonlinear terms, the coupled Duffing system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop systems in sliding modes. When the bounds of external disturbances are known, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces; When the bounds of external disturbances are unknown, two fuzzy logic tuning controllers (FLC) are introduced into SMC so that the switching gains of the SMC scheme are adjusted by FLC to response to any change in the input signals according to linguistic rules, then the SMC scheme is turned into the fuzzy sliding mode controller (FSMC) scheme. This method allows us to arbitrarily direct the parameters ).λi (i=1,2,3,4) onto any desired values. The results of numerical simulation are proved to show the effectiveness of the proposed methods.