In this article, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima.

Second-order necessary conditions in Pontryagin form for optimal control problems / Bonnans, J. Frédéric; Dupuis, Xavier; Pfeiffer, Laurent. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 52:6(2014), pp. 3887-3916. [10.1137/130923452]

Second-order necessary conditions in Pontryagin form for optimal control problems

DUPUIS, XAVIER;
2014

Abstract

In this article, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima.
Second-order necessary conditions in Pontryagin form for optimal control problems / Bonnans, J. Frédéric; Dupuis, Xavier; Pfeiffer, Laurent. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 52:6(2014), pp. 3887-3916. [10.1137/130923452]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/160735
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