Variational maximum principle in the problem of optimal control of nonlinear wave processes
The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 3, pp. 105-117 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present necessary optimality condition in form of variational maximum principle for the problem of optimal control of nonlinear wave equation with nonlinear boundary conditions of first, second and third types.
Keywords: optimal control, wave equation, variational maximum principle.
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V. A. Terletsky; E. A. Lutkovskaya. Variational maximum principle in the problem of optimal control of nonlinear wave processes. The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 3, pp. 105-117. http://geodesic.mathdoc.fr/item/IIGUM_2010_3_3_a9/

[1] K. T. Akhmedov, S. S. Akhiev, “Neobkhodimye usloviya optimalnosti dlya nekotorykh zadach teorii optimalnogo upravleniya”, Dokl. AN AzSSR, 28:5 (1972), 12–16 | MR | Zbl

[2] O. V. Vasilev, V. A. Srochko, V. A. Terletskii, Metody optimizatsii i ikh prilozheniya, v. 2, Optimalnoe upravlenie, Nauka, Novosibirsk, 1990, 151 pp. | MR

[3] A. I. Egorov, “Ob optimalnom upravlenii v nekotorykh sistemakh s raspredelennymi parametrami”, Avtomatika i telemekhanika, 25:5 (1964), 613–623 | Zbl

[4] I. P. Natanson, Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974, 480 pp. | MR

[5] V. I. Plotnikov, V. I. Sumin, “Optimizatsiya ob'ektov s raspredelennymi parametrami, opisyvaemykh sistemami Gursa–Darbu”, Zhurn. vychisl. matematiki i mat. fiziki, 12:1 (1972), 61–77 | MR

[6] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978, 688 pp. | MR

[7] V. A. Terletskii, “Variatsionnyi printsip maksimuma v upravlyaemykh sistemakh odnomernykh giperbolicheskikh uravnenii”, Izv. vuzov. Matematika, 1999, no. 12, 82–90 | MR

[8] V. A. Terletskii, E. A. Lutkovskaya, “Obobschennoe reshenie nelineinogo volnovogo uravneniya s nelineinymi granichnymi usloviyami pervogo, vtorogo i tretego rodov”, Differents. uravneniya, 45:3 (2009), 403–415 | MR | Zbl

[9] V. A. Terletskii, “Obobschennoe reshenie odnomernykh polulineinykh giperbolicheskikh sistem so smeshannymi usloviyami”, Izv. vuzov. Matematika, 2004, no. 12, 75–83 | MR