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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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Contributor : Chadi Nour <>
Submitted on : Wednesday, December 17, 2003 - 12:33:11 PM
Last modification on : Tuesday, November 19, 2019 - 2:46:29 AM
Long-term archiving on: : Monday, September 20, 2010 - 11:49:50 AM


  • HAL Id : tel-00003973, version 2



Chadi Nour. L'équation de Hamlilton-Jacobi en contrôle optimal : dualité et géodésiques. Mathematics [math]. Université Claude Bernard - Lyon I, 2003. English. ⟨tel-00003973v2⟩



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