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S-convergence in the theory of homogenization of problems of optimal control

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Abstract

We give a definition of homogenized problems of optimal control in terms of variational S-limits and establish sufficient conditions for a family of problems of optimal control described by nonlinear operator relations to be compact with respect to the operation of homogenization.

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References

  1. J. L. Lions, Some Methods in the Mathematical Analysis of Systems and Their Control, Scientific Press, Beijing (1981).

    MATH  Google Scholar 

  2. L. D. Akulenko, Asymptotic Methods for Optimal Control [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  3. U. E. Raitum, Problems of Optimal Control for Elliptic Equations [in Russian], Zinatne, Riga (1989).

    Google Scholar 

  4. G. Buttazzo and G. Dal Maso, “Γ-convergence and optimal control problems,” JOTA, 38, No. 3, 385–407 (1982).

    Article  MATH  Google Scholar 

  5. P. I. Kogut, “Variational S-convergence of minimization problems. Part I. Definitions and basic properties,” Probl. Upravl. Informatiki, No. 5, 29–43 (1996).

    MathSciNet  Google Scholar 

  6. P. I. Kogut, “Variational S-convergence of minimization problems. Part II. Definitions and basic properties,” Probl. Upravl. Informatiki, No. 3, 78–90 (1997).

    MathSciNet  Google Scholar 

  7. V. I. Ivanenko and V. S. Mel’nik, Variational Methods in Problems of Control for Systems with Distributed Parameters [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  8. J. L. Lions, Contrôle des Systèmes Distribués Singuliers, Bordas, Paris (1983).

    MATH  Google Scholar 

  9. V. V. Fedorchuk and V. V. Fillipov, General Topology. Basic Structures [in Russian], Moscow University, Moscow (1988).

    Google Scholar 

  10. G. Dal Maso, Introduction to Γ-Convergence, Birkhäuser, Boston (1993).

    Google Scholar 

  11. P. I. Kogut, “S-convergence of problems of conditional minimization and its variational properties,” Probl. Upravl. Informatiki, No. 4, 64–79 (1997).

    MathSciNet  Google Scholar 

  12. H. Attouch, Variational Convergence for Functions and Operations, Pitman, London (1984).

    Google Scholar 

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Authors
  1. P. I. Kogut
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Additional information

Dnepropetrovsk Technical University of Railway Transport, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 11, pp. 1488–1498, November, 1997.

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Kogut, P.I. S-convergence in the theory of homogenization of problems of optimal control. Ukr Math J 49, 1671–1681 (1997). https://doi.org/10.1007/BF02487505

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  • DOI: https://doi.org/10.1007/BF02487505

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