Runge–Kutta model-based nonlinear observer for synchronization and control of chaotic systems

This paper proposes a novel nonlinear gradient-based observer for synchronization and observer-based control of chaotic systems. The model is based on a Runge–Kutta model of the chaotic system where the evolution of the states or parameters is derived based on the error-square minimization. The stability and convergence conditions of observer and control methods are analyzed using a Lyapunov stability approach. In numerical simulations, the proposed observer and well-known sliding-mode observer are compared for the synchronization of a Lü chaotic system and observer-based stabilization of a Chen chaotic system. The noisy case for synchronization and parameter uncertainty case for stabilization are also considered for both observer-based methods.