L'équation de Hamilton-Jacobi en contrôle optimal
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 resu...
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| Format: | masterThesis |
| Published: |
2003
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| Online Access: | http://hdl.handle.net/10725/7407 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php https://tel.archives-ouvertes.fr/tel-00003973/ |
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| Summary: | 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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