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Time delayed repetitive learning control for chaotic systems. (English) Zbl 1051.93528

In this paper, a time-delayed repetitive learning control (RLC) technique for stabilizing unstable periodic orbits has been proposed. The main advantage of the integration of RLC and time-delayed feedback control is that the controller is able to adaptively learn, from learning cycles, an appropriate control force. Unlike the conventional RLC, the new controller does not require exact knowledge (analytic representation) of the target unstable periodic orbit, except the time constant, which however can be easily identified via either experiments or adaptive learning techniques. All these together make the new design a viable technique for chaos control.

MSC:

93D15 Stabilization of systems by feedback
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[1] DOI: 10.1007/978-1-4615-5629-9 · doi:10.1007/978-1-4615-5629-9
[2] DOI: 10.1109/81.244908 · Zbl 0800.93758 · doi:10.1109/81.244908
[3] DOI: 10.1016/S0167-2789(96)00197-2 · Zbl 0894.58040 · doi:10.1016/S0167-2789(96)00197-2
[4] DOI: 10.1142/S0218127498001972 · Zbl 0940.93036 · doi:10.1142/S0218127498001972
[5] DOI: 10.1080/002071700405914 · Zbl 1006.93599 · doi:10.1080/002071700405914
[6] DOI: 10.1016/0375-9601(92)90745-8 · doi:10.1016/0375-9601(92)90745-8
[7] DOI: 10.1080/002071700405842 · Zbl 1006.93557 · doi:10.1080/002071700405842
[8] Yu X., IEEE Trans. Circuits Syst. I 46 pp 1408–
[9] X. Yu, Y.P. Tian and G. Chen, Controlling Chaos and Bifurcations in Engineering Systems, ed. G. Chen (CRC Press, Boca Raton, FL, 1999) pp. 255–274.
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