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On the variational characterization of switching points. (English) Zbl 1081.49019

The paper deals with a measurable extremal control satisfying the Pontryagin maximum principle in the point-to-point time-optimal problem for a class of smooth nonlinear in phase variables and control systems. A notion of a switching function is derived which has under some conditions the property: all switching points of a measurable extremal control are contained in the set of its zeros.

MSC:

49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
58E25 Applications of variational problems to control theory
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