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Stabilization of periodic orbits in discrete and continuous-time systems

Abstract : The main problem evaluated in this manuscript is the stabilization of periodic orbits of non-linear dynamical systems by use of feedback control. The goal of the control methods proposed in this work is to achieve a stable periodic oscillation. These control methods are applied to systems that present unstable periodic orbits in the state space, and the latter are the orbits to be stabilized.The methods proposed here are such that the resulting stable oscillation is obtained with low control effort, and the control signal is designed to converge to zero when the trajectory tends to the stabilized orbit. Local stability of the periodic orbits is analyzed by studying the stability of some linear time-periodic systems, using the Floquet stability theory. These linear systems are obtained by linearizing the trajectories in the vicinity of the periodic orbits.The control methods used for stabilization of periodic orbits here are the proportional feedback control, the delayed feedback control and the prediction-based feedback control. These methods are applied to discrete and continuous-time systems with the necessary modifications. The main contributions of the thesis are related to these methods, proposing an alternative control gain design, a new control law and related results.
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https://tel.archives-ouvertes.fr/tel-00852424
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Submitted on : Wednesday, August 21, 2013 - 9:52:12 AM
Last modification on : Tuesday, April 16, 2019 - 6:16:03 AM
Long-term archiving on: : Friday, November 22, 2013 - 2:55:17 AM

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Thiago Perreira das Chagas. Stabilization of periodic orbits in discrete and continuous-time systems. Other [cond-mat.other]. Université Paris Sud - Paris XI; Instituto Tecnológico de Aeronáutica, 2013. English. ⟨NNT : 2013PA112085⟩. ⟨tel-00852424⟩

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