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Quadratic order conditions for bang-singular extremals

M.-Soledad Aronna (aronna***at***cmap.polytechnique.fr)
J.-Frederic Bonnans (frederic.bonnans***at***inria.fr)
Andrei V. Dmitruk (avdmi***at***cemi.rssi.ru)
Pablo A. Lotito (plotito***at***exa.unicen.edu.ar)

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.

Keywords: optimal control, second order condition, control constraint, singular arc, bang-singular solution

Category 1: Infinite Dimensional Optimization

Citation: NUMERICAL ALGEBRA, CONTROL AND OPTIMIZATION Volume 2, Number 3, September 2012 pp. 511–546 doi:10.3934/naco.2012.2.511 INRIA Research Report N° 7664 (2011) http://hal.inria.fr/inria-00605128/en/

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Entry Submitted: 07/06/2011
Entry Accepted: 07/06/2011
Entry Last Modified: 08/24/2012

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