When does relaxation reduce the minimum cost of an optimal control problem?

Abstract : Relaxation is a regularization procedure used in optimal control, involving the replacement of velocity sets by their convex hulls, to ensure the existence of a minimizer. It can be an important step in the construction of sub-optimal controls for the original, unrelaxed, optimal control problem (which may not have a minimizer), based on obtaining a minimizer for the relaxed problem and approximating it. In some cases the infimum cost of the unrelaxed problem is strictly greater than the infimum cost over relaxed state trajectories; there is a need to identify such situations because then the above procedure fails. Following on from earlier work by Warga, we explore the relation between, on the one hand, non-coincidence of the minimum cost of the optimal control and its relaxation and, on the other, abnormality of necessary conditions (in the sense that they take a degenerate form in which the cost multiplier set to zero).
Type de document :
Communication dans un congrès
52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.526-531, 2013, proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6759935〉
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Contributeur : Estelle Bouzat <>
Soumis le : mardi 23 septembre 2014 - 16:00:47
Dernière modification le : lundi 21 mars 2016 - 17:50:25

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Michele Palladino, Richard Vinter. When does relaxation reduce the minimum cost of an optimal control problem?. 52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.526-531, 2013, proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6759935〉. 〈hal-01067548〉

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