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MULTIPOINT DIFFERENTIAL RELATIONS USING FOR SEARCHING OF THE HAMILTON TYPE EQUATION SOLUTION SINGULARITIES

Annotation

Properties of nonsmooth problems of control and geometric optics (formalized as the Dirichlet boundary problems) are studied. Apparat for multipoint differential relations finding and constructing is developed. Multipoint differential relations appears in an analyze of control problems and differential games, which often have many motions starting from one point. Efficiency of the developed method is illustrated on the example planar velocity problem with ninconvex target sets, which may have boarders with different differential properties.

Keywords

Dirichlet boundary problem; mininimax solution; eikonal; velocity problem; singular set; control; the 1st order PDE

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UDC

517.977.1

Pages

1261-1263

References

1. Subbotin A.I. Obobshhennye reshenija uravnenij v chastnyh proizvodnyh pervogo porjadka. Perspektivy dinamicheskoj optimizacii. Moskva; Izhevsk: Institut komp'juternyh tehnologij, 2003. 336 s. 2. Ushakov V.N., Uspenskij A.A., Lebedev P.D. Postroenie minimaksnogo reshenija uravnenija tipa jejkonala // Trudy Instituta matematiki i mehaniki. 2008. T. 14, № 2. S. 182-191. 3. Kruzhkov S.N. Obobshhennye reshenija uravnenij Gamil'tona-Jakobi tipa jejkonala, I // Matem. sbornik. 1975. T. 98. Vyp. 3. S. 450-493. 4. Sljusarev G.G. Geometricheskaja optika. M.: Izdatel'stvo Akademii nauk SSSR, 1946. 332 s. 5. Uspenskij A.A., Lebedev P.D. Postroenie funkcii optimal'nogo rezul'tata v zadache bystrodejstvija na osnove mnozhestva simmetrii // Avtomatika i telemehanika. 2009. № 7. S. 50-57. 6. Brus Dzh., Dzhiblin P. Krivye i osobennosti. M.: Mir, 1988. 262 s. 7. Ushakov V.N., Uspenskij A.A., Lebedev P.D. Geometrija singuljarnyh krivyh dlja odnogo klassa zadach bystrodejstvija // Vestn. Sankt-Peterburgskogo un-ta. 2013. Ser. 10. Vyp. 3. S. 157–167.

Received

2015-05-13

Section of issue

Scientific articles

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