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.

I. Introduction

Pecora and Carroll, [1], have proposed a master-slave strategy for chaos synchronization, although the characteristic of chaotic systems would conflict the synchronization design. The widespread methods in this context are the adaptive control [2], the sliding mode control [3], the robust interval observer [4], the gravitational search algorithm filter [5], etc. Besides, applying the state observer approach for chaos synchronization seems to be a challenging task. The authors in [6] proved that estimating the chaotic systems via nonlinear state observer techniques is achievable. Actually, the chaotic transmitter is considered as a nonlinear dynamical systems, while its receiver is contemplated as an observer of the driving system, see for instance [7].