Geodesic
Algorithms for solving the velocity problem
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 4, pp. 387-397

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We study the performance control problem with a piecewise constant dynamics and a non-convex target set with a smooth boundary. A non-smooth solution to the problem is formed on the basis of the constructions of the theory of mathematical control and the principles of geometric optics. Statements are proved that reveal the geometry of singular curves, as well as their differential properties. Algorithms for constructing a singular set and an optimal result function are proposed and implemented. The effectiveness of the algorithms is illustrated by the results of the software package.
Keywords: optimal control, velocity, dispersing curve, plane-layered medium, optimal result function, Snelius law. 
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     author = {P. D. Lebedev and A. A. Uspenskii},
     title = {Algorithms for solving the velocity problem},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {387--397},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_4_a1/}
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P. D. Lebedev; A. A. Uspenskii. Algorithms for solving the velocity problem. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 4, pp. 387-397. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_4_a1/