Composite adaptive fuzzy control for synchronizing generalized Lorenz systems

Abstract

This paper presents a methodology of asymptotically synchronizing two uncertain generalized

Lorenz systems via a single continuous composite adaptive fuzzy controller (AFC). To facilitate

controller design, the synchronization problem is transformed into the stabilization problem by

feedback linearization. To achieve asymptotic tracking performance, a key property of the optimal

fuzzy approximation error is exploited by the Mean Value Theorem. The composite AFC, which

utilizes both tracking and modeling error feedbacks, is constructed by introducing a series-parallel

identification model into an indirect AFC. It is proved that the closed-loop system achieves

asymptotic stability under a sufficient gain condition. Furthermore, the proposed approach cannot

only synchronize two different chaotic systems but also significantly reduce computational

complexity and implemented cost. Simulation studies further demonstrate the effectiveness of the

proposed approach.