A Novel Approach for Synchronizing of Fractional Order Uncertain Chaotic Systems in the Presence of Unknown Time-Variant Delay and Disturbance

Abstract

This paper presents a new method for synchronizing between two fractional order chaotic systems in the simultaneous presence of three categories including uncertainty, external disturbance and time-varying delay. The uncertainties considered in chaotic drive and response systems are on the nonlinear functions, the external disturbances are finite with unknown upper bound,  and the delays in the nonlinear functions are 1- variable with time 2- unknown and 3- different from each other in two drive and response systems. A new hybrid method based on fuzzy, adaptive and robust techniques is proposed to achieve synchronization for a specific class of fractional order chaotic systems. The fuzzy method is used to estimate the effects of uncertainties and delayed functions, the adaptive method is employed to obtain the optimal weights of the fuzzy approximator as well as the estimation for upper bound of disturbances, and the robust method is performed to ensure the stability of synchronization and also to cover the errors of both fuzzy and adaptive methods. Simulation in MATLAB environment shows the efficiency of the proposed method in achieving the synchronization goal despite the problems of delay, disturbance and uncertainty.