Fixed-time terminal synergetic observer for synchronization of fractional-order chaotic systems

In this paper, a fixed-time terminal synergetic observer for synchronization of fractional-order nonlinear chaotic systems is proposed. First, fixed-time terminal attractors for fractional-order nonlinear systems are introduced on the basis of fixed-time stability of integer-order nonlinear differential equations and on defining particular fractional-order macro-variables. Second, a new synergetic observer dedicated to the synchronization of fractional-order chaotic systems is developed. The proposed observer converges in a predefined fixed-time uniformly bounded with respect to initial conditions. Thanks to the step-by-step procedure, only one communication channel is used to achieve the synchronization. Third, a fixed-time synergetic extended observer with unknown input is constructed to simultaneously estimate the state variables and to recover the unknown input. Finally, computer simulations are performed to illustrate the efficiency of the proposed synchronization method and its application in a secure communication scheme.