Adaptive synchronization for a class of uncertain fractional order chaotic systems with random perturbations: theory and experiment

Synchronization of fractional-order chaotic systems with parameter uncertainty and random disturbance is investigated in the paper. The bound of the external disturbance is assumed to be unknown in advance and it is tackled through an adaptive control process. Based on the adaptive control techniques and fractional-order stability theorem, a general adaptive controller is designed to guarantee the synchronization of such nonlinear fractional systems. The controller is simple to design and implement, and only few state information is required. Finally, an illustrative example is proposed to demonstrate the effectiveness and feasibility of the presented scheme by both Matlab simulation and experimental result.