Adaptive Sliding Synchronization of Duffing-Holmes Fractional Order Chaotic Systems with Uncertainty and the Fractional Order Sliding Surface

In this paper, the problem of adaptive sliding synchronization of Duffing-Holmes fractional order chaotic systems is investigated in the presence of uncertainty, disturbance with the fractional order sliding surface. Master and Slave systems dynamics include uncertainty. In this design, the adaptive sliding control method is used. At first, the upper bound of uncertainty and disturbance in the slave system is estimated and compensated, then a new fractional order sliding surface is designed for two systems synchronization as the slave system can fallow the master system. Despite the presence of uncertainty and disturbance, the proposed adaptive sliding mode controller guarantees the asymptotic stability of synchronization error and boundedness of close loop signals with the fractional order sliding surface. Finally, simulation results show the effectiveness and correctness of the control method presented in synchronization of two Duffing-Holmes fractional order chaotic systems together with the fractional order sliding surface and the estimation of the system uncertainty.