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Continuous parametrization of attainable sets by solutions of differential inclusions. (English) Zbl 0953.34012

Summary: It is shown that if the Hamiltonian corresponding to a differential inclusion is sufficiently regular and solutions reaching the points in the boundary of the set which are attainable at some fixed time, are unique then the parametrization mentioned in the title exists – it is continuous with respect to the points attained at that time. No such parametrization may exist if at least one point of the boundary is reached by more than one solution.

MSC:

34A60 Ordinary differential inclusions
93B03 Attainable sets, reachability
54C60 Set-valued maps in general topology
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
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