Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator

In this paper, fast global fixed-time terminal sliding mode control for the synchronization problem of a generalized class of nonlinear perturbed chaotic systems has been investigated with the application of memristor-based oscillator in the presence of external disturbances and unmodeled dynamics. In the fixed-time control strategy, unlike conventional asymptotic or finite-time approaches, convergence time is not related to the initial conditions. In the designed global fixed-time controller, both the sliding phase and reaching phase have fixed-time convergence characteristics and consequently, via the proposed strategy, precise synchronization of the master-slave systems is accomplished within fixed convergence time. The fast fixed-time synchronization problem of the nonlinear memristor chaotic system (MCS) has been investigated. In the first stage, an in-circuit emulator (ICE) for the considered memristor is utilized in order to apply on the defined MCSs. In the next stage, according to the considered ICE, the dynamical structure of the MCS is formulated along with the fixed-time synchronization problem which is efficiently addressed via the designed controller in the presence of external disturbances and unmodeled dynamics. Finally, the strength and validity of the theoretical outcomes are confirmed through numerical simulations.