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Detailed view PhD thesis
Institut National Polytechnique de Toulouse - INPT (04/11/2005), Noailles Joseph (Dir.)
Attached file list to this document: 
PDF
These.pdf(20.1 MB)
Thesis.pdf(20 MB)
ANNEX
Soutenance.pdf(9.3 MB)
Defense.pdf(9.3 MB)
Resolution numerique de problemes de controle optimal par une methode homotopique simpliciale
Pierre Martinon1

On s'interesse ici a la resolution numerique de problemes de controle optimal peu reguliers. On utilise a la base les methodes dites indirectes, a la fois precises et rapides, mais en pratique tres sensibles a l'initialisation. Cette difficulte nous amene a utiliser une demarche homotopique, dans laquelle on part d'un probleme apparente plus facile a resoudre. Le "suivi de chemin" de l'homotopie connectant les deux problemes est ici realise par un algorithme de type simplicial. On s'interesse en premier lieu a un probleme de transfert orbital avec maximisation de la masse utile, puis a deux problemes d'arcs singuliers. Les perspectives futures liees a ces travaux comprennent en particulier l'etude de problemes a contraintes d'etat, egalement delicats a resoudre par les methodes indirectes. Par ailleurs, on souhaite comparer cette approche avec les methodes directes, qui impliquent la discretisation totale ou partielle du probleme.
1:  IRIT - Institut de recherche en informatique de Toulouse
controle optimal – methodes de tir – principe du Maximum – controle bang-bang – arcs singuliers – homotopie – methode simpliciale.
http://www.enseeiht.fr/lima/apo/martinon/docs/These.pdf

Numerical resolution of optimal control problems by a simplicial homotopy method
This study deals with the numerical resolution of optimal control problems with a low regularity. We primarily use indirect methods, which are both fast and accurate, but suffer from a great sensitiveness to the initialization. This difficulty leads us to introduce a continuation approach, in which we start from a related, but easier to solve problem. The path following between the two problems is here implemented with a simplicial method. We first study an orbital transfer problem with payload maximization, then two singular arcs problems. The future perspectives related to this work include in particular the study of state constraints problems, which are difficult to solve with indirect methods. Also, we would like to compare this approach with direct methods, which imply total or partial discretization of the problem.
optimal control – shooting methods – Maximum principle – bang-bang control – singular arcs – continuation – simplicial method.

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