Necessary optimality conditions for average cost minimization problems

Piernicola Bettiol; Nathalie Khalil

doi:10.3934/dcdsb.2019086

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2019, Volume 24, Issue 5: 2093-2124. Doi: 10.3934/dcdsb.2019086

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Necessary optimality conditions for average cost minimization problems

Piernicola Bettiol^1, and
Nathalie Khalil^2,

1.
Laboratoire de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200 Brest, France
2.
MODAL'X, Université Paris Ouest Nanterre La Défense, 200 Avenue de la République, 92001 Paris Nanterre, France

Dedicated to U. Ledzewicz, H. Maurer and H. Schättler

Received: January 2018

Revised: January 2019

Early access: March 2019

Published: March 2019

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Abstract

Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an average cost, providing a paradigm which differs from the more traditional minimax or robust optimization criteria. In this paper, we provide necessary optimality conditions for a nonrestrictive class of optimal control problems in which unknown parameters intervene in the dynamics, the cost function and the right end-point constraint. An important feature of our results is that we allow the unknown parameters belonging to a mere complete separable metric space (not necessarily compact).

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Mathematics Subject Classification: Primary: 49J15.

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