Abstract
The estimation of the complex-valued coefficient in a nonstationary equation of quasioptics by the least squares method is investigated. An analog of Pontryagin’s maximum principle is shown to be true for such estimates.
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M. A. Vorontsov and I. I. Shmal’gauzen, Principles of Adaptive Optics [in Russian], Nauka, Moscow (1985).
T. Yu. Shameeva, “Optimization in the problem on a light beam propagating in an inhomogeneous medium,” Vestn. Mosk. Univ., Ser. Vych. Mat. Kibern., No. 1, 12–19 (1985).
A. D. Iskenderov and G. Ya. Yagubov, “A variational method to solve the inverse problem of determining the quantum-mechanical potential,” DAN SSSR, 303, No. 5, 1044–1048 (1988).
A. D. Iskenderov and G. Ya. Yagubov, “Optimal control of nonlinear quantum-mechanical systems,” Avtom. Telemekh., No. 12, 27–38 (1989).
G. Ya. Yagubov and M. A. Musaeva, “A variational method to solve a multidimensional inverse problem for the nonlinear Schrödinger equation,” Izv. AN Azerb., Ser. Fiz.–Tekhn. i Mat. Nauk, 15, No. 5–6, 58–61 (1994).
G. Ya. Yagubov and M. A. Musaev, “An identification problem for the nonlinear Schrödinger equation,” Diff. Uravneniya, 33, No. 12, 1691–1698 (1997).
A. D. Iskenderov and G. Ya. Yagubov, “Optimal control of quantum-mechanical potential,” Tr. IMM ANA, 18, 75–80 (1998).
G. Ya. Yagubov and N. S. Ibragimov, “Optimal control problem for the nonstationary equation of quasioptics,” in: Problems of Mathematical Modeling and Optimal Control [in Russian], Baku (2001), pp. 49–57.
O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
I. C. Gohberg and M. G. Krein, Theory and Applications of Volterra Operators in Hilbert Space, Amer. Math. Soc. (1970).
L. P. Nizhnik, Inverse Nonstationary Scattering Problem [in Russian], Naukova Dumka, Kyiv (1973).
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).
V. I. Plotnikov, “The first variation and conjugate problem in optimal control theory,” Funkts. Analiz i ego Prilozheniya, Issue 10, No. 4, 95–96 (1976).
V. I. Plotnikov and E. R. Sikorskaya, “Optimization of a controlled object described by a nonlinear system of hyperbolic equations,” Izv. VUZov, Ser. Radiofizika, 15, No. 3, 345–357 (1972).
S. M. Nikol’skii, A Course of Mathematical Analysis [in Russian], Vol. 2, Nauka, Moscow (1973).
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2012, pp. 142–154.
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Ibrahimov, N.S. Necessary condition of pontryagin’s maximum principle type in the identification problem for a nonstationary equation of quasioptics. Cybern Syst Anal 48, 441–451 (2012). https://doi.org/10.1007/s10559-012-9423-x
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DOI: https://doi.org/10.1007/s10559-012-9423-x