Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control

This paper deals with a finite time robust synchronization problem of a class of uncertain fractional chaotic/hyper-chaotic systems with a novel fractional sliding mode control technique. Firstly, a fractional order sliding surface is proposed to mimic the behavior of master chaotic system. Then, a fractional order sliding mode control (FOSMC) methodology is derived analytically for convergence of all the synchronizing errors to zero in finite time. Finally, the derived control strategy is augmented with an auxiliary control based on uncertainty and disturbance estimator (UDE) for ensuring the robustness of the closed loop system dynamics in the presence of system uncertainties. Further, the uncertainties with unknown bounds are tackled for depicting the practical scenario and these results are also applicable to the N-dimensional uncertain chaotic as well as hyper-chaotic systems. Moreover, Mittag-Leffler and fractional order Lyapunov results are utilized to prove the stability and finite time convergence. Also, the proposed method delivers chatter-free control signal which is a major issue in sliding mode. MATLAB simulations are carried out to verify the efficacy and robustness of the derived results by considering two examples from literature.