Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique

In this paper, the problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.