Optimal control and admissible relaxation for subdifferential evolution inclusions |
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Authors: | Tiziana Cardinali Nikolaos S Papageorgiou |
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Institution: | (1) Department of Mathematics, Perugia University, Via Vantitelli 1, 06123 Perugia, Italy;(2) Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece |
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Abstract: | In this paper we study the relaxation of optimal control problems monitored by subdifferential evolution inclusions. First
under appropriate convexity conditions, we establish an existence result. Then we introduce the relaxed problem and show that
it always has a solution under fairly general hypotheses on the data. Subsequently we examine when the relaxation is admissible.
So we show that every relaxed trajectory can be approximated by extremal original ones (i.e. original trajectories generated
by bang-bang controls) and that the values of the original and relaxed problems are equal. Some examples are also presented. |
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Keywords: | Primary 49A20 |
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