Robust fixed-time synchronization of fractional order chaotic using free chattering nonsingular adaptive fractional sliding mode controller design

In this paper, fixed-time synchronization of two fractional order chaotic systems in the presence of uncertainties and exogenous disturbances using a fuzzy adaptive sliding mode controller has been investigated. In the proposed approach, the upper bound of the synchronization time is completely independent of the difference between the initial conditions of the master and slave systems and just depends on the design parameters of the switching surface and controller. Adaption laws are proposed for selecting controllers and switching surface parameters to have a proper control and reduce control dependence on estimation of disturbances upper bound. Furthermore, to remove chattering phenomenon a fuzzy logic system is used. The fixed-time stability and controller design are driven based on Lyapunov stability theorem and simulations results are provided to show the effectiveness of proposed method.