Second-Order Optimality Conditions for Broken Extremals and Bang-Bang Controls

Abstract : We survey the results on no-gap second order optimality conditions (both necessary and sufficient) in the Calculus of Variations and Optimal Control, that were obtained in the monographs [31] and [40], and discuss their further develop-ment. First, we formulate such conditions for broken extremals in the simplest prob-lem of the Calculus of Variations and then, we consider them for discontinuous con-trols in optimal control problems with endpoint and mixed state-control constraints, considered on a variable time interval. Further, we discuss such conditions for bang-bang controls in optimal control problems, where the control appears linearly in the Pontryagin-Hamilton function with control constraints given in the form of a con-vex polyhedron. Bang-bang controls induce an optimization problem with respect to the switching times of the control, the so-called Induced Optimization Problem. We show that second-order sufficient condition for the Induced Optimization Problem together with the so-called strict bang-bang property ensure second-order sufficient conditions for the bang-bang control problem. Finally, we discuss optimal control problems with mixed control-state constraints and control appearing linearly. Tak-ing the mixed constraint as a new control variable we convert such problems to bang-bang control problems. The numerical verification of second-order conditions is illustrated on three examples.
Type de document :
Communication dans un congrès
FPG 13, 2013, Krakow, Poland. Proceedings of the 16th French-German-Polish Conference on Optimization. 〈http://www.fgp13.agh.edu.pl〉
Liste complète des métadonnées

Littérature citée [42 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01101295
Contributeur : Estelle Bouzat <>
Soumis le : jeudi 8 janvier 2015 - 12:21:19
Dernière modification le : lundi 21 mars 2016 - 11:33:26
Document(s) archivé(s) le : jeudi 9 avril 2015 - 10:35:31

Fichier

Osmolovskii-Maurer_FGP13.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01101295, version 1

Collections

Citation

Nikolai Osmolovskii, Helmut Maurer. Second-Order Optimality Conditions for Broken Extremals and Bang-Bang Controls. FPG 13, 2013, Krakow, Poland. Proceedings of the 16th French-German-Polish Conference on Optimization. 〈http://www.fgp13.agh.edu.pl〉. 〈hal-01101295〉

Partager

Métriques

Consultations de la notice

169

Téléchargements de fichiers

112