Quadratic order conditions  for bang-singularextremals

M. Soledad Aronna; J. Frédéric Bonnans; Andrei V. Dmitruk; Pablo A. Lotito

doi:10.3934/naco.2012.2.511

Article Contents

2012, Volume 2, Issue 3: 511-546. Doi: 10.3934/naco.2012.2.511

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Quadratic order conditions for bang-singular extremals

1.
CONICET CIFASIS, Argentina, INRIA Saclay - CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau
2.
INRIA Saclay - CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau
3.
Russian Academy of Sciences - CEMI and Moscow State University, 47 Nakhimovsky Prospect, 117418 Moscow
4.
CONICET PLADEMA - Univ. Nacional de Centro de la Prov. de Buenos Aires, Campus Universitario Paraje Arroyo Seco, B7000 Tandil

Received: July 2011

Revised: June 2012

Published: July 2012

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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.

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Mathematics Subject Classification: Primary: 49K15.

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