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On attainable states of systems with discrete control and a constraint concerning the number of switchings. (Russian) Zbl 0567.49020
Finite-dimensional and distributed control systems, Collect. sci. Works, Kiev 1983, 130-134 (1983).
[For the entire collection see Zbl 0531.00014.]
The paper deals with systems with discrete control and a constraint concerning the number of switchings. The statement of this problem is typical for applications. The author investigates a system which is defined by pairs of vector fields on a smooth manifold (dimension $$k\geq 3)$$ and also shows that the number of switchings is related to an analytical description of the generalized set of reachability for small times.
Reviewer: L.Asmykovitch
##### MSC:
 93B03 Attainable sets, reachability 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 93B05 Controllability 57R27 Controllability of vector fields on $$C^\infty$$ and real-analytic manifolds