Simultaneously Robust Chaos Synchronization and Identification of Unknown Parameters for Nonlinear Gyro System

Abstract

This paper concerns robust synchronization and parameter identification for nonlinear gyroscope systems. Gyros are widely utilized in navigational applications where synchronization plays a vital role. A system of nonlinear dynamical equations with some parameters presents a model of gyro systems. The parameters of gyro can vary in time, which can lead to desynchronization of the gyro systems. In this paper, we assume that a gyro system has bounded time-varying unknown parameters and the synchronization problem is considered in two situations. First, the synchronization of two gyroscopes with identical dynamical model and, second, the synchronization of a gyroscope with the Rössler system. The Lyapunov stability theory with control terms is employed to cope with the problem. Also, the identification of time-varying unknown parameters is the side goal of the paper. The proposed scheme synchronizes chaotic nonlinear systems in both situations appropriately. In addition, the slave parameters converge to the nominal values of master parameters despite uncertainty. Simulation results illustrate the superiority of the proposed method.