A Chaos Control Method by DFC Using State Prediction

The Delayed Feedback Control method (DFC) proposed by Pyragas applies an input based on the difference between the current state of the system, which is generating chaos orbits, and the $\tau$-time delayed state, and stabilizes the chaos orbit into a target. In DFC, the information about a position in the state space is unnecessary if the period of the unstable periodic orbit to stabilize is known. There exists the fault that DFC cannot stabilize the unstable periodic orbit when a linearlized system around the periodic point has an odd number property. There is the chaos control method using the prediction of the $\tau$-time future state (PDFC) proposed by Ushio et al. as the method to compensate this fault. Then, we propose a method such as improving the fault of the DFC. Namely, we combine DFC and PDFC with parameter W, which indicates the balance of both methods, not to lose each advantage. Therefore, we stabilize the state into the $\tau$ periodic orbit, and ask for the ranges of Wand gain K using Jury' method, and determine the quasi-optimum pair of (W, K) using a genetic algorithm. Finally, we apply the proposed method to a discrete-time chaotic system, and show the efficiency through some examples of numerical experiments.