Adaptive terminal sliding mode control for synchronization of a chaotic mechanical system with input nonlinearity

In this paper, the problem of finite-time chaos synchronization for centrifugal flywheel governor with lumped perturbation and control input nonlinearity is investigated. First, a terminal sliding surface is introduced and its finite-time convergence to the equilibrium point is proved. Then, a fuzzy logic system is employed to approximate the lumped perturbation including model uncertainty and external disturbance, therefore, it relax the requirement of the exact model. Afterwards, based on the adaptive laws and finite-time control idea, a robust adaptive terminal sliding mode controller is proposed to enforce the occurrence of the sliding motion in a given finite time and it also ensure the synchronization tracking-error on the terminal sliding surface to converge to a small neighborhood of equilibrium point in 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, simulation results demonstrate the effectiveness of the proposed control scheme.