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On the attainable set of differential inclusions and control systems. (English) Zbl 0636.49018

The reachable sets of a time-dependent differential inclusion defined on a separable Banach space X are considered and some properties of the minimum-time map are proved. Under suitable hypotheses results analogous to the ones true in the finite dimensional case are given. Moreover, if X is finite dimensional a bang-bang theorem and a characterization of the attainable sets by means of the minimum-time map are obtained for multivalued inclusions satisfying additional assumptions.
Reviewer: G.Stefani

MSC:

93B03 Attainable sets, reachability
34A60 Ordinary differential inclusions
93B05 Controllability
46B99 Normed linear spaces and Banach spaces; Banach lattices
49J27 Existence theories for problems in abstract spaces
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93C10 Nonlinear systems in control theory
93C25 Control/observation systems in abstract spaces
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