A robust controller for chaotic systems under external excitation

We show that one can control a chaotic system under external force excitation to arbitrary trajectories, even when the desired trajectories are not located on the embedded orbits of a chaotic system. The method utilizes a newly developed sliding mode controller with a time-varying manifold dynamic to offer a feedback control in compensation with the external excitation, and drive the system orbits to desired states. The proposed controller does not need high gain to suppress the external force, and meanwhile, keeps robustness against parameter uncertainty and noise disturbance as does the traditional sliding mode control. Simulations are provided to illustrate the performance of the controller.