Chaos Synchronization of Uncertain Fractional-Order Chaotic Systems With Time Delay Based on Adaptive Fuzzy Sliding Mode Control

This paper proposes an adaptive fuzzy sliding mode control (AFSMC) to synchronize two different uncertain fractional-order time-delay chaotic systems, which are infinite dimensional in nature, and time delay is a source of instability. Because modeling the behavior of dynamical systems by fractional-order differential equations has more advantages than integer-order modeling, the adaptive time-delay fuzzy-logic system is constructed to approximate the unknown fractional-order time-delay-system functions. By using Lyapunov stability criterion, the free parameters of the adaptive fuzzy controller can be tuned online by output-feedback-control law and adaptive law. The sliding mode design procedure not only guarantees the stability and robustness of the proposed AFSMC, but it also guarantees that the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.