Quadratic conditions for bang-singular extremals

Maria Soledad Aronna; J. Frederic Bonnans; Andrei V. Dmitruk; Pablo Lotito

inria-00605128, version 3

Quadratic conditions for bang-singular extremals

Maria Soledad Aronna () ^1, 2, 3, J. Frederic Bonnans () ^1, 2, Andrei V. Dmitruk () ^4, 5, Pablo Lotito ⁶

Numerical Algebra, Control and Optimization, AIMS Journal 2, 3 (2012) 511-546

Abstract: This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.

1: COMMANDS (INRIA Saclay - Ile de France)
INRIA – CNRS : UMR7641 – Polytechnique - X – ENSTA ParisTech
2: Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
Polytechnique - X – CNRS : UMR7641
3: Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas (CIFASIS)
CONICET and Universidad Nacional de Rosario and Universidad Paul Cézanne Aix-Marseille III
4: Central Economics and Mathematics Institute (CEMI)
Russian Academy of Science
5: Faculty of Computational Mathematics and Cybernetics (Lomonosov Moscow State University)
Moscow State University
6: Plasmas Densos Magnetizados (PLADEMA)
CONICET – Universidad Nacional del Centro de la Provincia de Buenos Aires

inria-00605128, version 3
http://hal.inria.fr/inria-00605128
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From: Maria Soledad Aronna <>
Submitted on: Monday, 2 July 2012 17:08:49
Updated on: Thursday, 27 September 2012 10:01:04

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arXiv: 1107.0161

DOI: 10.3934/naco.2012.2.511

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%F inria-00605128, version 3
%0 Journal Article
%U http://hal.inria.fr/inria-00605128
%2 MATH:MATH_OC
%T Quadratic conditions for bang-singular extremals
%A Aronna, Maria Soledad
%A Bonnans, J. Frederic
%A Dmitruk, Andrei V.
%A Lotito, Pablo
%+ COMMANDS - INRIA Saclay - Ile de France , Centre de Mathématiques Appliquées - Ecole Polytechnique - CMAP , Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas - CIFASIS , Central Economics and Mathematics Institute - CEMI , Faculty of Computational Mathematics and Cybernetics - Lomonosov Moscow State University , Plasmas Densos Magnetizados - PLADEMA
%X This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.
%2 Dans ce travail nous étudions le problème de commande optimale avec des contrôles aﬃnes dans la dynamique. On considère des contraintes de non-négativité sur la commande et une quantité ﬁnie de contraintes d'égalité et d'inégalité sur la valeur ﬁnale de l'état. Premièrement on obtient des conditions nécessaires d'optimalité de second ordre. Ensuite, on présente une condition suﬃsante pour le cas d'une commande scalaire.
%G English
%J Numerical Algebra, Control and Optimization, AIMS Journal
%8 2012-09-01
%2 international
%I American Institute for Mathematical Sciences
%2 A special issue dedicated to Professor Helmut Maurer on the occasion of his 65th. birthday
%V 2
%N 3
%P 511-546
%R 10.3934/naco.2012.2.511
%2 Published in Numerical Algebra, Control and Optimization, AIMS, special issue in honor of Helmut Maurer, Volume 2, Issue 3, p.p. 511 - 546, 2012.
%K Optimal control; second order conditions; control constraints; singular arc; bang-singular solutions, SADCO
%2 2011-06-30
%Z RR-7664
%2 84242

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Quadratic conditions for bang-singular extremals

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