Two-stage adaptive finite-time modified function projective lag synchronization of chaotic systems

In this article, using the adaptive control technique and the sliding-mode variable structure control scheme, the finite-time modified function projective lag synchronization of chaotic systems with fully unknown parameters and unknown bounded disturbances is realized through two stages. First, a sliding surface is established to ensure the sliding mode is finite-time stable. Afterwards, by the aid of finite-time control theory and Lyapunov stability theorem, an appropriate adaptive law is designed to ensure the sustained sliding motion occurs in a limited time and the unknown parameters are tackled well. Finally, a simulation is put forward to demonstrate the correctness and effectiveness of the proposed scheme.