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Chaos control in the uncertain Duffing oscillator. (English) Zbl 1243.93086
Summary: 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.

MSC:
93D15 Stabilization of systems by feedback
34H10 Chaos control for problems involving ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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