Input–output linearization minimum sliding mode error feedback control for synchronization of chaotic system

Abstract

Under the existence of system uncertainties and external disturbances, complete synchronization of chaotic systems is achieved by introducing a novel input–output linearization minimum sliding mode error feedback control with high control precision, which is based on the input–output linearization method and sliding mode control. In the literature, the magnitudes of bounded nonlinear dynamics of synchronous error system were required in the designed sliding mode controller. In this study, this article proposed a new approach to estimate the various uncertainties and disturbances on the basis of chaotic system. To facilitate the analysis, the concept of equivalent control error is introduced, which is the key to the utilization of input–output linearization minimum sliding mode error feedback control. A cost function is formulated on the basis of the principle of minimum sliding mode covariance constraint; then, the equivalent control error is estimated and fed back to the conventional sliding mode. It is shown that the sliding mode after the input–output linearization minimum sliding mode error feedback control will approximate to the ideal sliding mode, resulting in improved control performance and quality. Finally, the chaotic gyro system and chaotic FitzHugh–Nagumo neurons system have been employed to verify the proposed controller. Sufficient conditions to guarantee stable synchronization are given and the numerical simulations of complete synchronization of the two chaotic systems are performed to verify the effectiveness of the presented schemes.