Recursive backstepping control of chaotic Duffing oscillators

In this paper, the dynamics of a forced Duffing oscillator are studied by means of modern nonlinear, bifurcation and chaos theories to show that the system is ultimately experiencing chaos. The main objective is to characterize and control this chaotic behavior. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Systematic following of a reference model is introduced. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally a discussion and conclusions are given with possible future extensions.