Geodesic
On a time-optimal control for the generalized Dubins car
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 26-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the problem of time-optimal approach of a fourth-order nonlinear system describing the motion of an airplane in a horizontal plane to two fixed points in a given order.
Keywords: control, nonlinear object, approach. 
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Yu. I. Berdyshev. On a time-optimal control for the generalized Dubins car. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 26-35. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a2/

[1] Dubins L.E., “On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents”, Amer. J. Math., 79 (1957), 497–516 | DOI | MR | Zbl

[2] Berdyshev Iu.I., “Time-optimal control synthesis for a fourth-order nonlinear system”, J. Appl. Math. Mech., 39:6 (1975), 948–956 | DOI | MR | Zbl

[3] Khamza M.Kh., Kolas I., Rungalder V., “Optimalnye po bystrodeistviyu traektorii poleta v zadache presledovaniya”, Upravlenie kosmicheskimi apparatami i korablyami, Nauka, M., 1971, 410–418

[4] Aizeks R., Differentsialnye igry, Mir, M., 1967, 497 pp. | MR

[5] Markov A.A., “Neskolko primerov resheniya osobogo roda zadach o naibolshikh i naimenshikh velichinakh”, Soobschenie Kharkov. mat. obschestva Ser. 2., 1:5, 6 (1889), 250–276

[6] L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mischenko, Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961, 384 pp. | MR

[7] Berdyshev Yu.I., Sintez optimalnogo po bystrodeistviyu upravleniya dvizheniem materialnoi tochki v srede s soprotivleniem, dis.. kand. fiz.-mat. nauk, IMM UNTs AN SSSR, Sverdlovsk, 1978, 133 pp.

[8] Berdyshev Yu.I., Nelineinye zadachi posledovatelnogo upravlenie i ikh prilozhenie, IMM UrO RAN, Ekaterinburg, 2015, 193 pp.

[9] Li E.B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972, 576 pp. | MR

[10] Berdyshev Yu.I., “Ob odnoi zadache posledovatelnogo obkhoda nelineinym upravlyaemym ob'ektom sovokupnosti gladkikh mnogoobrazii”, Differents. uravneniya, 38:11 (2002), 1–11 | MR