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A new method for stabilizing unstable periodic orbits of continuous-time systems. Application to control of chaos

Thiago P. Chagas 1 Pierre-Alexandre Bliman 2 Karl H. Kienitz 3
1 UESC - Universidade Estadual De Santa Cruz [Brazil]
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
Inria Paris-Rocquencourt
3 ITA - Instituto Tecnológico de Aeronáutica [São José dos Campos]
Abstract : This work presents a new method of stabilization for unstable periodic orbits of continuous-time dynamical systems. The principle of this method is to use feedback term based on the difference between the actual state value and the future state value computed along the trajectories of the uncontrolled system. To compute the value of the latter, an implicit Runge-Kutta ODE integration method is used, giving rise to a time-varying dynamical controller. The stability of the control method is defined in terms of the Floquet theory and the conditions for calculation of the monodromy matrix are presented. Numerical results are obtained using the forced Van der Pol oscillator as case study and the orthogonal collocation method as implicit Runge-Kutta method.
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Conference papers
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https://hal.inria.fr/hal-00761338
Contributor : Pierre-Alexandre Bliman <>
Submitted on : Wednesday, December 5, 2012 - 12:48:59 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM

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Thiago P. Chagas, Pierre-Alexandre Bliman, Karl H. Kienitz. A new method for stabilizing unstable periodic orbits of continuous-time systems. Application to control of chaos. CDC 2012 - 51st IEEE Conference on Decision and Control, Dec 2012, Maui, HI, United States. pp.2146-2151, ⟨10.1109/CDC.2012.6426456⟩. ⟨hal-00761338⟩

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