Geodesic
The method of tracking domains in search problems
Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 225-246 
A. G. Chkhartishvili; E. V. Shikin. The method of tracking domains in search problems. Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 225-246. http://geodesic.mathdoc.fr/item/SM_1995_80_1_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new, geometric approach to solving dynamical search problems is proposed. On the example of certain two-dimensional search problems it is shown how, using the method proposed, one can find sufficient conditions guaranteeing detection, as well as determining the corresponding trajectories and the necessary time.

[1] Aizeks R., Differentsialnye igry, Mir, M., 1967 | MR

[2] Kim D. P., Metody poiska i presledovaniya podvizhnykh ob'ektov, Nauka, M., 1989 | MR

[3] Petrosyan L. A., Garnaev A. Yu., Igry poiska, Iz-vo S.-Peterb. un-ta, SPb., 1992 | MR

[4] Zalgaller V. A., Teoriya ogibayuschikh, Nauka, M., 1975 | MR | Zbl

[5] Brus Dzh., Dzhibli N. P., Krivye i osobennosti, Mir, M., 1988 | MR

[6] Chkhartishvili A. G., “Ob odnom geometricheskom svoistve sledyaschei oblasti v zadachakh poiska”, Vestn. MGU. Ser. 1. Matematika, mekhanika, 1992, no. 3, 7–10 | MR | Zbl

[7] Chkhartishvili A. G., Ob odnom geometricheskom svoistve sledyaschei oblasti v dvumernoi zadache poiska, Dep. VINITI. No 60-B91, M., 1991

[8] Poznyak E. G., Shikin E. V., Differentsialnaya geometriya. Pervoe znakomstvo, Iz-vo MGU, M., 1990

[9] Chernousko F. L., “Upravlyaemyi poisk podvizhnogo ob'ekta”, Prikl. matematika i mekhanika, 44:1 (1980), 3–12 | MR | Zbl

[10] Gubaidullin S. M., Shikin E. V., “Sledyaschaya oblast na tsilindre i na tore”, Vestn. MGU. Ser. 15. Vychisl. matematika i kibernetika, 1992, no. 2, 46–50 | MR | Zbl

[11] Olshanskii V. K., “Igra presledovaniya s ogranicheniem na kriviznu traektorii i chislo manevrov presleduyuschego”, Avtomatika i telematematika, 1972, no. 8, 16–22

[12] Breakwell J. V., Merz A. W., “Toward a Complete Solution of the Homicidal Chauffeur Game”, Proc. 1 st. Intern. Conf. on Theory and Appl. of Diff. Games, Amherst, Mass., 1969 | Zbl