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On the stable reconstruction of controls in nonlinear distributed systems

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Abstract

This paper deals with the problem of the dynamic approximation of the disturbances acting on a distributed system. A solution algorithm which is stable with respect to informational noise and computing errors is proposed. Examples are given to illustrate the basic constructions.

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References

  1. Krasovski, N. N., andSubbotin, A. I.,Game-Theoretical Control Problems, Springer Verlag, New York, New York, 1987.

    Google Scholar 

  2. Krasovski, N. N.,Controlling of Dynamical Systems, Nauka, Moscow, Russia, 1985 (in Russian).

    Google Scholar 

  3. Osipov, Yu. S. Differential Games for Hereditary Systems, Doklady, Akademii Nauk SSSR, Vol. 196, pp. 761–768, 1971 (in Russian).

    Google Scholar 

  4. Osipov, Yu. S.,On the Theory of Differential Games for Systems with Distributed Parameters, Doklady Akademii Nauk SSSR, Vol. 223, pp. 1314–1317, 1975 (in Russian).

    Google Scholar 

  5. Ivanov, V. K., Vasin, V. V., andTanana, V. P.,Theory of Ill-posed Problems and Applications, Nauka, Moscow, Russia, 1978 (in Russian).

    Google Scholar 

  6. Tikhonov, A. N., andArsenin, V. Ya.,Solution of Ill-Posed Problems, Wiley, New York, New York, 1977.

    Google Scholar 

  7. Osipov, Yu. S., andKryazhimski, A. V.,On the Dynamical Solution of Operator Equations, Doklady Akademii Nauk SSSR, Vol. 269, pp. 552–556, 1983 (in Russian).

    Google Scholar 

  8. Osipov, Yu. S., andKryazhimski, A. V.,Method of Lyapunov Functions for Modelling Problems of Motion, 4th Chetaev Conference on Motion Stability, Zvenigorod, Russia, p. 35, 1982 (in Russian).

  9. Kryazhimski, A. V., andOsipov, Yu. S.,On Modelling the Control in a Dynamical System, IKN SSSR, Tekhnicheskaya Kibernetika, Vol. 2, pp. 51–60, 1983 (in Russian).

    Google Scholar 

  10. Kryazhimski, A. V., andOsipov, Yu. S.,On the Method of Positional Modelling of Control in Dynamic Systems, Qualitative Issues of the Theory of Differential Equations and Controlled Systems, Ural Scientific Center, Russian Academy of Sciences, Sverdlovsk, Russia, pp. 34–44, 1988 (in Russian).

    Google Scholar 

  11. Osipov, Yu. S.,Control Problems under Insufficient Information, Proceedings of the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987; Springer, Berlin, Germany, 1988.

    Google Scholar 

  12. Osipov, Yu. S.,Inverse Problems of Dynamics for Systems Described by Parabolic Inequalities, Report WP-89-101, IIASA, Laxenburg, Austria, 1989.

    Google Scholar 

  13. Osipov, Yu. S., Kryazhimski, A. V., andMaksimov, V. I.,Dynamic Regularization Problems for Distributed Parameter Systems, Preprint, Institute of Mathematics and Mechanics, Ural Scientific Center, Russian Academy of Sciences, Sverdlovsk, Russia, 1991 (in Russian).

    Google Scholar 

  14. Maksimov, V. I.,On Dynamical Modelling of Unknown Disturbances in Parabolic Inequalities, Prikladnaya Matematika i Mekhanika Vol. 52, pp. 743–750, 1988 (in Russian).

    Google Scholar 

  15. Kim, A. V., Korotki, A. I., andOsipov, Yu. S.,Inverse Problems of Dynamics for Parabolic Systems, Prikladnaya Matematika i Mekhanika, Vol. 54, pp. 754–759, 1990 (in Russian).

    Google Scholar 

  16. Korbiz, Y. S., Maksimov, V. I., andOsipov, Yu. S.,Dynamic Control Modelling in Some Parabolic Systems, Prikladnaya Matematika i Mekhanika, Vol. 54, pp. 355–360, 1990 (in Russian).

    Google Scholar 

  17. Lakshmikantham, V., andLeela, S.,Nonlinear Differential Equations in Abstract Spaces, International Series in Nonlinear Mathematics, Pergamon Press, Oxford, England, Vol. 2, 1981.

    Google Scholar 

  18. Benilan, P.,Solutions Integrales d'Equations d'Evolution dans un Espace de Banach, Comptes Rendus de l'Academie des Sciences, Vol. 274, pp. 47–50, 1972.

    Google Scholar 

  19. Benilan, P.,Equations d'Evolution dans un Espace de Banach Quelconque et Applications, Thèse, Orsay, France, 1972.

  20. Vrabie, I. I.,A Compactness Criterion in C(0, T; X) for Subsets of Solutions of Nonlinear Evolution Equations Governed by Accretive Operators, Rendiconti del Seminario Matematico, Università e Politecnio di Torino, Vol. 43, pp. 149–157, 1985.

    Google Scholar 

  21. Gaevskii, H., Greger, K., andZakharias, K.,Nonlinear Operator Equations and Operator Differential Equations, Mir, Moscow, Russia, 1978 (in Russian).

    Google Scholar 

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Authors and Affiliations

  1. Moscow University, Moscow, Russia

    Yu. S. Osipov (Professor)

  2. Russian Academy of Sciences, Moscow, Russia

    Yu. S. Osipov (Professor)

  3. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, Russia

    V. I. Maksimov (Professor and Head of Laboratory)

Authors
  1. Yu. S. Osipov
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  2. V. I. Maksimov
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Communicated by N. V. Banichuk

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Osipov, Y.S., Maksimov, V.I. On the stable reconstruction of controls in nonlinear distributed systems. J Optim Theory Appl 82, 485–501 (1994). https://doi.org/10.1007/BF02192214

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  • DOI: https://doi.org/10.1007/BF02192214

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