Quadratic conditions for bang-singular extremals

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

inria-00605128, version 1

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

N° RR-7664 (2011)

Abstract: This paper deals with optimal control problems for systems aﬃne in the control variable. We have 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 get a second order sufficient condition for the scalar control case. The results use in an essential way the Goh transformation.

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 1
http://hal.inria.fr/inria-00605128
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From: Maria Soledad Aronna <>
Submitted on: Thursday, 30 June 2011 16:48:17
Updated on: Monday, 19 December 2011 11:03:55

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arXiv: 1107.0161

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Quadratic conditions for bang-singular extremals

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