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Planification de mouvements pour les systèmes non-holonomes et étude de la contrôlabilité spectrale pour les équations de Schrödinger linéarisées

Abstract : Abstract : The objective of this thesis is, firstly, to provide motion planning algorithms for nonholonomic systems, and secondly, to study the spectral controllability for the linearized Schrödinger equations. We made a double contribution to the problem of motion planning for nonholonomic systems. Based on the sub- Riemannian geometry , we have developed a new algorithm that completely solves the problem in a general framework. We have also proposed a numerical implementation of the continuation method that provides satisfactory solutions to the rollingbody problem, a classic example of nonholonomic systems with two inputs. We have given necessary and sufficient conditions of spectral controllability in finite time for the linearized Schrödinger equations in dimension 2 and 3. Their genericity with respect to the domain has been studied by a novel technique based on integral equations.
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Submitted on : Tuesday, October 5, 2010 - 7:49:12 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM
Long-term archiving on: : Thursday, January 6, 2011 - 2:58:51 AM

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  • HAL Id : tel-00523628, version 1

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Ruixing Long. Planification de mouvements pour les systèmes non-holonomes et étude de la contrôlabilité spectrale pour les équations de Schrödinger linéarisées. Mathématiques [math]. Ecole Polytechnique X, 2010. Français. ⟨tel-00523628⟩

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