Investigation of regularity conditions in optimal control problems with geometric mixed constraints |
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| Authors: | AV Arutyunov DYu Karamzin FL Pereira |
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| Institution: | 1. Faculty of Natural Science, Peoples’ Friendship University of Russia, Moscow, Russia.;2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia.;3. Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia.;4. Department of Applied Mathematics, Univ Estadual Paulista – UNESP, S?o José do Rio Preto, Brazil.;5. Faculdade de Engenharia da Universidade do Porto, Porto, Portugal. |
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| Abstract: | We investigate regularity conditions in optimal control problems with mixed constraints of a general geometric type, in which a closed non-convex constraint set appears. A closely related question to this issue concerns the derivation of necessary optimality conditions under some regularity conditions on the constraints. By imposing strong and weak regularity condition on the constraints, we provide necessary optimality conditions in the form of Pontryagin maximum principle for the control problem with mixed constraints. The optimality conditions obtained here turn out to be more general than earlier results even in the case when the constraint set is convex. The proofs of our main results are based on a series of technical lemmas which are gathered in the Appendix. |
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| Keywords: | regularity conditions optimal control mixed constraints geometric constraints |
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