Sliding Mode Disturbance Observer Control Based on Adaptive Hybrid Projective Compound Combination Synchronization in Fractional-Order Chaotic Systems

Abstract

In this paper, the hybrid projective compound combination synchronization (HPCCS) in a class of commensurate fractional-order chaotic Genesio–Tesi system with unknown disturbance has been investigated. To deal with the problem of bounded disturbance, the nonlinear HPCCS is proposed for the fractional-order chaotic system. Further, by choosing the appropriate control gain parameters, the nonlinear fractional-order disturbance observer can approximate the disturbance efficiently. Based on the sliding mode control (SMC) method, a simple sliding mode surface has been introduced. Moreover, by using the Lyapunov stability theory, the designed adaptive SMC method establishes that the states of the three master and two chaotic slave systems are synchronized expeditiously. Finally, some numerical simulation results are illustrated to visualize the effectiveness and the utility of the developed approach on the considered system in the presence of the external unknown bounded disturbances using MATLAB.