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Optimal relaxed controls for systems governed by impulsive differential inclusions. (English) Zbl 1092.49002
Summary: We consider optimal control problems for a class of impulsive systems governed by differential inclusions on Banach spaces. For each fixed control policy, we prove the existence of a nonempty set of solutions for the system. Using this we then prove the existence of optimal controls for certain control problems including min-max games. The paper is concluded with some comments on open problems in the area.

MSC:
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
49J27 Existence theories for problems in abstract spaces
34A60 Ordinary differential inclusions
34G20 Nonlinear differential equations in abstract spaces
34K30 Functional-differential equations in abstract spaces
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