# American Institute of Mathematical Sciences

May  2019, 24(5): 2093-2124. doi: 10.3934/dcdsb.2019086

## Necessary optimality conditions for average cost minimization problems

 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 Published  March 2019

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).

Citation: Piernicola Bettiol, Nathalie Khalil. Necessary optimality conditions for average cost minimization problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2093-2124. doi: 10.3934/dcdsb.2019086
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