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Theses

L'équation de Hamlilton-Jacobi en contrôle optimal : dualité et géodésiques

Abstract : The main object of this thesis is the application of new methods from nonsmooth analysis and which use the Hamilton-Jacobi equation for the study of certain problems in control theory. There are three parts in our work: * In the first part we develop a new duality result in control theory. This result generalizes, in a number of ways, the Vinter's duality (1993) and gives a new characterization of the minimal time function. * The second part is devoted to the study of the Hamilton-Jacobi equation of minimal time, but in a domain which contains the origin. We prove the existence of (minimal) solutions of this equation and we show that these solutions are closely linked to global geodesics trajectories. * In the third part, we study the existence of minimal loop trajectories for a control system. We give a necessary and sufficient conditions for the existence of this type of trajectories at a given point.
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https://tel.archives-ouvertes.fr/tel-00003973
Contributor : Chadi Nour <>
Submitted on : Monday, December 15, 2003 - 1:06:23 PM
Last modification on : Tuesday, October 22, 2019 - 8:26:02 AM
Long-term archiving on: : Friday, April 2, 2010 - 7:19:34 PM

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  • HAL Id : tel-00003973, version 1

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Chadi Nour. L'équation de Hamlilton-Jacobi en contrôle optimal : dualité et géodésiques. Mathematics [math]. Université Claude Bernard - Lyon I, 2003. English. ⟨tel-00003973v1⟩

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