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New Feedback Laws for Stabilization of Unstable Periodic Orbits

Abstract : In this note a gain tuning scheme for prediction-based chaos control of discrete-time systems is proposed, extending previous work by T. Ushio and S. Yamamoto. The derived control laws are proved to be stabilizing. Three different time-invariant or time-varying laws are proposed, leading to different convergence rates and sizes for the basins of attraction. The results are illustrated by numerical simulations. A parallel between finding unstable periodic orbits and chaos control is done.
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Thiago Pereira das Chaga, Pierre-Alexandre Bliman, Karl-Heinz J. Kienitz. New Feedback Laws for Stabilization of Unstable Periodic Orbits. 8th IFAC Symposium on Nonlinear Control Systems (2010), Sep 2010, Bologna, Italy. ⟨10.3182/20100901-3-IT-2016.00139⟩. ⟨hal-00793631⟩



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