On Feedback Control of Chaotic Continuous-Time Systems

In this paper, we further extend the ideas and techniques developed previously by the present authors for controlling discrete-time chaotic dynamic systems using traditional feedback control strategies to continuous-time chaotic systems. We study how the conventional engineering approach using canonical feedback controllers can control the chaotic trajectory of a continuous-time nonlinear system to converge to its equilibrium points and, more significantly, to its multiperiodic orbits including unstable limit cycles. We describe our approach via a detailed investigation of the chaotic Duffing equation, with special emphasis on the control of its chaotic trajectory to one of its multiperiodic orbits. Finally, we provide a rigorous mathematical theory and some computer simulations to support and visualize such controllability of the Duffing equation. © 1993 IEEE