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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.

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