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Optimization of distributed systems in Lebesgue space

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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], Nauka, Moscow (1961).

    Google Scholar 

  2. A. Ya. Dubovitskii and A. A. Milyutin, “Extremal problems in the presence of constraints,” Zh. Vychisl. Mat. Mat. Fiz.,5, No. 3, 395–453 (1965).

    Google Scholar 

  3. Z. W. Neustadt, “An abstract variational theory with application to a broad class of optimization problems. I: General theory,” SIAM J. Control,4, 505–527 (1966).

    Google Scholar 

  4. R. V. Gamkrelidze and G. L. Kharatishvili, “Extremal problems in linear topological spaces,” Izv. Akad. Nauk SSSR, Ser. Mat.,33, No. 4, 781–839 (1969).

    Google Scholar 

  5. A. G. Butkovskii, Theory of the Optimal Control of Distributed Parameter Systems [in Russian], Nauka Moscow (1965).

    Google Scholar 

  6. J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag (1971).

  7. K. A. Lur'e, Optimal Control in Problems of Mathematical Physics [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  8. T. K. Sirazetdinov, Optimization of Distributed Parameter Systems, [in Russian], Nauka, Moscow, (1977).

    Google Scholar 

  9. A. I. Egorov, Optimal Control of Heat Conduction and Diffusion Processes, [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  10. V. I. Plotnikov, “A unified method of proving necessary and sufficient conditions for optimality for controllable systems with lumped and distributed parameters,” in: Proc. All-Union Conference on Problems of Theoretical Cybernetics [in Russian], Novosibirsk (1969).

  11. V. I. Plotnikov, “Necessary conditions for optimality for controllable systems of a general form,” Dokl. Akad. Nauk SSSR,199, No. 2, 275–278 (1971).

    Google Scholar 

  12. V. I. Plotnikov, “Necessary and sufficient conditions for optimality and conditions for the uniqueness of optimizing functions for controllable systems of a general form,” Izv. Akad. Nauk SSSR, Ser. Mat.,36, No. 3, 652–679 (1972).

    Google Scholar 

  13. V. I. Plotnikov and V. I. Sumin, “Optimization of plants with distributed parameters, described by Goursat-Darboux systems,” Zh. Vychisl. Mat. Mat. Fiz.,12, No. 1, 61–77 (1972).

    Google Scholar 

  14. V. A. Yakubovich, “Certain variants of the abstract maximum principle,” Dokl. Akad. Nauk SSSR,229, No. 4, 816–819 (1976).

    Google Scholar 

  15. V. A. Yakubovich, “On an abstract theory of optimal control. I,” Sib. Mat. Zh.,18, No. 3, 685–707 (1977); V. A. Yakubovich, “On an abstract theory of optimal control. II,” ibid. Sib. Mat. Zh.,19, No. 2, 436–480 (1978).

    Google Scholar 

  16. A. S. Matveev and V. A. Yakubovich, “The optimal control of certain distributed systems,” Sib. Mat. Zh.,19, No. 5, 1109–1140 (1978).

    Google Scholar 

  17. J. Warga, Optimal Control of Differential and Functional Equations, Academic Press (1972).

  18. J. Persson, “Noncharacteristic Cauchy problems and generalized Goursat problems in Rn,” J. Math. Mech.,18, No. 11, 1087–1094 (1969).

    Google Scholar 

  19. S. F. Morozov and V. I. Sumin, “Nonlinear integrodifferential equation of nonstationary transport,” Mat. Zametki,21, No. 5, 665–676 (1977).

    Google Scholar 

  20. S. F. Morozov and V. I. Sumin, “Nonlinear systems of integrodifferential equations for nonstationary transport,” Sib. Mat. Zh.,19, No. 4, 842–848 (1978).

    Google Scholar 

  21. V. I. Plotnikov and V. I. Sumin, “On the first variation and the dual probiem in the theory of optimal control,” Funkts. Anal. Prilozhen.,10, No. 4, 95–96 (1976).

    Google Scholar 

  22. M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow, (1966).

    Google Scholar 

  23. N. Dunford and J. T. Schwartz, Linear Operators. Pt. 1. General Theory, Wiley (1958).

  24. J. L. Daleckii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Am. Math. Soc. (1974).

  25. V. I. Plotnikov and V. I. Sumin, “Problems of the stability of nonlinear Goursat-Darboux systems,” Differents. Uravn.,8, No. 5, 845–856 (1972).

    Google Scholar 

  26. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  27. V. I. Sumin, “Optimization of controllable generalized Volterra systems,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Gorkii (1975).

  28. G. I. Bell and S. Glasstone, Nuclear Reactor Theory, Van Nos Reinhold (1970).

  29. S. F. Morozov and V. I. Sumin, “The optimization of nonlinear transport processes,” Dokl. Akad. Nauk SSSR,247, No. 4, 794–798 (1979).

    Google Scholar 

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Gorki State University. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 22, No. 6, pp. 142–161, November–December, 1981.

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Plotnikov, V.I., Sumin, V.I. Optimization of distributed systems in Lebesgue space. Sib Math J 22, 913–929 (1981). https://doi.org/10.1007/BF00968060

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