Optimal Control Problems with Weakly Converging Input Operators in A Nonreflexive Framework

Lorenzo Freddi

Abstract: The variational convergence of sequences of optimal control problems with state constraints (namely inclusions or equations) with weakly converging input multi-valued operators is studied in a nonreflexive abstract framework, using $\G$-convergence techniques. This allows to treat a lot of situations where a lack of coercivity forces to enlarge the space of states where the limit problem has to be imbedded. Some concrete applications to optimal control problems with measures as controls are given either in a nonlinear multi-valued or nonlocal but single-valued framework.

Keywords: Optimal Control; $\Gamma$-convergence; functionals defined on measures; weak convergence; multi-valued operators; inclusions.

Classification (MSC2000): 49J45.

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