Chaos control in the uncertain Duffing oscillator

A robust control scheme is developed for the well-known chaotic Duffing equation subject to uncertainties. Based on Lyapunov stability theory, sufficient conditions for tracking a smooth periodic orbit have been analyzed theoretically and numerically. The robust feedback control law is composed of a dynamic compensator and a linearizing control law including estimation of uncertainties. The control time is explicitly computed. Simulation results are presented to verify the validity of the proposed scheme.