Vakhrameev, S. A.; Topunov, M. V. On the variational characterization of switching points. (English) Zbl 1081.49019 J. Math. Sci., New York 112, No. 5, 4558-4574 (2002). 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. Reviewer: Ernst G. Al’brekht (Ekaterinburg) Cited in 2 Documents MSC: 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 58E25 Applications of variational problems to control theory Keywords:time-optimal problem; extremal control; switching points PDFBibTeX XMLCite \textit{S. A. Vakhrameev} and \textit{M. V. Topunov}, J. Math. Sci., New York 112, No. 5, 4558--4574 (2002; Zbl 1081.49019) Full Text: DOI