Controlling chaotic trajectories to unstable limit cycles - A case study

In the last two years, we have developed some new ideas and techniques for the control of chaotic nonlinear systems using conventional feedback controllers design methods, for both discrete-time and continuous-time systems [1-4], where the target position is either an (unstable) equilibrium point or an (unstable) limit cycle of the chaotic system. In this paper, we further provide a rigorous mathematical theory to support these new ideas and techniques, for a particular yet representative case: the well-known continuous-time chaotic Duffing system.