Fixed-time supper twisting disturbance observer and sliding mode control for a secure communication of fractional-order chaotic systems

This paper proposed a new disturbance observer (DO) based on the fixed-time supper-twisting algorithm (FTSTA) for rejecting perturbations of secure communication of the fractional-order chaotic systems (FOCSs). First, the FOCSs are remodeled into the Takagi–Sugeno fuzzy (TSF) system with the expectation of softening the calculations of the design of the controller and observer. Second, the synchronization control was designed based on the FTSTA sliding mode control (SMC). Third, a new DO for the secure communication system (SCS) of FOCSs was proposed to estimate the disturbance on public channels and uncertainty variations. Fourth, the stability of the proposed synchronization control was obtained by using the Lyapunov condition. Finally, to verify the correction of the proposed method, the MATLAB simulation with the use of FONCOM toolbox was used to meet the desired expectations of theoretically proposed method. There are, small reaching times, small steady-states, and most tested disturbances and parameters’ variations were compensated by the proposed DO.