Geodesic
Geometry of singular curves for one class of velocity
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 157-167

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Both numerical and analytical algorithms for approximate solutions of differential games and control problems are proposed using convex and nonsmooth analyze methods. Algorithms of optimal result function calculation in the velocity problem with circle vectogramme are considered. These algorithms are based on symmetry sets. Smooth properties of these sets are studied, the equation of tangent in their regular points are written. Application of the results investigated for numerical construction of generalized (minimax) solutions of Dirichlet boundary problems for Hamilton type PDE is suggested. The examples of velocity problems are calculated. Bibliogr. 23. Il. 5.
Keywords: velocity problem, singular curve, nonsmoothness.
Mots-clés : tangent 
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     author = {V. N. Ushakov and A. A. Uspenskiy and P. D. Lebedev},
     title = {Geometry of singular curves for one class of velocity},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a15/}
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V. N. Ushakov; A. A. Uspenskiy; P. D. Lebedev. Geometry of singular curves for one class of velocity. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 157-167. http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a15/