Adaptive finite-time modified function projective lag synchronisation with definite attenuation rate for uncertain chaotic systems

This paper investigates the adaptive finite-time modified function projective lag synchronisation with definite attenuation rate for a class of chaotic systems with unknown parameters. Firstly, a novel integral type terminal sliding surface is proposed to ensure the finite-time stability of the sliding motion. Subsequently, an adaptive finite-time control law is designed to guarantee the occurrence of the sliding motion in a limited time and the accurate estimation of the unknown parameters. Moreover, the exponential attenuation rate designed in this paper can further cut down the synchronisation time. Numerical simulations are presented to verify the feasibility and effectiveness of the proposed method.