The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System with Stochastic Disturbances and Unknown Parameters

Abstract

This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part considers that the drive-response systems have the same or different dimensions. Firstly, a FO sliding surface is established in terms of the fractional calculus. Secondly, depending on the FO Lyapunov stability theory and the sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed. They can ensure that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed, and the upper bound values of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the scheme via MATLAB.