Non-dominated sorting genetic algorithm for the high gain observer optimization. Application to chaos synchronization

The problem posed by this paper is the state synchronization of nonlinear perturbed chaotic systems by employing an optimal high gain observer, which optimization is derived by the non-dominated sorting genetic algorithm (NSGA-II). Such a procedure is proved to be an efficient multiobjective search technique in various applications. Thus, a new quadratic optimization criterion is proposed to calculate the required optimal value of the observer setting parameter θ that characterizes the observation gain. The adopted fitness function allows achieving a compromise between the observation error and the correction term of the high gain observer. Moreover, the stability of this designed approach is studied using the Lyapunov framework. Simulations are proposed to prove the efficiency of the proposed synchronization scheme on the well-known unified perturbed chaotic system.