Time-delayed chaos control with repetitive learning

In this paper, a time-delayed chaos control method based on repetitive learning is proposed. The integration of the repetitive learning control principle and the time delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to conventional repetitive learning control, no exact knowledge (analytic representation) of the target periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning methods. To facilitate the discussion, the typical chaotic Duffing system is used as an example for illustration of the general methodology. Simulation result is provided to show the effectiveness of the proposed approach.