Finite time synchronization of chaotic systems with unmatched uncertainties

In this paper, finite time synchronization of two chaotic systems with unmatched uncertainties is presented by using a terminal sliding mode controller. The error dynamics between the master chaotic system and the slave chaotic system is established firstly. Then a terminal sliding mode manifold and a control methodology are proposed to guarantee the state variables of the error dynamics to reach the sliding mode manifold in finite time, and then converge to the neighborhood of the equilibrium points in finite time along the sliding mode manifold. The mathematical relationship between the neighborhood of the equilibrium point and the range of the unmatched uncertainties and parameters of sliding mode is formulated. It is shown that the proposed controller is invariant to the matched uncertainties, and the controller can guarantee the error system to reach the neighborhood of the equilibrium points when unmatched uncertainties exist. Simulation results are presented to validate the design and the analysis.