Geodesic
On the structure of the singular set of solutions in one class of 3D time-optimal control problems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 471-486 Cet article a éte moissonné depuis la source Math-Net.Ru

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A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.
Keywords: time-optimal problem, dispersing surface, bisector, extreme point, curvature, singular set, Frene's trihedron.
Mots-clés : pseudo-vertex 
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     title = {On the structure of the singular set of solutions in one class of {3D} time-optimal control problems},
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A. A. Uspenskii; P. D. Lebedev. On the structure of the singular set of solutions in one class of 3D time-optimal control problems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 471-486. http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a8/

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