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Optimization of a controlled plant that can be described by a nonlinear system of hyperbolic equations

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Abstract

The necessary condition for optimality of control of a plant which can be described by a weakly nonlinear system of hyperbolic equations with constraints of the inequality type on the phase coordinates of the system at a stipulated finite time are derived.

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Literature cited

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  2. A. Ya. Dubovitskii and A. A. Milyutin, “Extremum problems in the presence of constraints,” Zh. Vychislitel'. Matem. i Matem. Fiz.,5, No. 3, 395 (1965).

    Google Scholar 

  3. A. A. Milyutin, “General schemes for obtaining the necessary extremum conditions, and problems in optimal control,” Usp. Matem. Nauk,25, No. 5, 110 (1970).

    Google Scholar 

  4. B. N. Pshenichnyi, “The dual method in extremal problems, 1,” Kibernetika, No. 3, 89 (1965).

    Google Scholar 

  5. O. A. Ladyzhenskaya, The Mixed Problem for a Hyperbolic Equation [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  6. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  7. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations [Russian translation], IL, Moscow (1958).

    Google Scholar 

  8. V. I. Plotnikov, “The energy inequality and the redefinability property of systems of eigenfunctions,” Izv. Akad. Nauk SSSR, Ser. Matem., 32, No. 4, 743 (1968).

    Google Scholar 

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Authors and Affiliations

  1. Gor'kii State University, USSR

    V. I. Plotnikov & E. R. Sikorskaya

Authors
  1. V. I. Plotnikov
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  2. E. R. Sikorskaya
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 3, pp. 346–357, March, 1972.

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Plotnikov, V.I., Sikorskaya, E.R. Optimization of a controlled plant that can be described by a nonlinear system of hyperbolic equations. Radiophys Quantum Electron 15, 256–265 (1972). https://doi.org/10.1007/BF02210664

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  • DOI: https://doi.org/10.1007/BF02210664

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