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Homogenization of Optimal Control Problems for Functional Differential Equations

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Abstract

The paper deals with the variational convergence of a sequence of optimal control problems for functional differential state equations with deviating argument. Variational limit problems are found under various conditions of convergence of the input data. It is shown that, upon sufficiently weak assumptions on convergence of the argument deviations, the limit problem can assume a form different from that of the whole sequence. In particular, it can be either an optimal control problem for an integro-differential equation or a purely variational problem. Conditions are found under which the limit problem preserves the form of the original sequence.

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References

  1. Kolmanovski{, V., and Myshkis, V., Applied Theory of Functional Differential Equations, Mathematics and Its Applications, Soviet Series, Kluwer Academic Publishers, Dordrecht, Holland, Vol. 85, 1992.

  2. Azbelev, N. V., Maksimov, V. P., and Rakhmatullina, L. F., Introduction to the Theory of Functional Differential Equations, Nauka, Moscow, Russia, 1991 (in Russian).

    Google Scholar 

  3. Buttazzo, G., and Freddi, L., Optimal Control Problems with Weakly Converging Input Operators, Discrete and Continuous Dynamical Systems, Vol. 1, pp. 401–420, 1995.

    Google Scholar 

  4. Drakhlin, M. E., and Stepanov, E., Γ-Convergence for a Class of Functionals with Deviating Argument, Journal of Convex Analysis (to appear).

  5. Dal Maso, G., An Introduction to Γ-Convergence, Birkhaüser, Boston, Massachussets, 1993.

    Google Scholar 

  6. Drakhlin, M. E., On Convergence of Sequences of Internal Superposition Operators, Functional Differential Equations, Vol. 1, pp. 83–94, 1993.

    Google Scholar 

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Author notes

  1. E. Stepanov

    Present address: Scuola Normale Superiore, Pisa, Italy

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    G. Buttazzo

  2. Research Institute, College of Judea and Samaria, Kedumim-Ariel, Israel

    M. E. Drakhlin

  3. Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy

    L. Freddi

  4. Institute of Fine Mechanics and Optics, St. Petersburg, Russia

    E. Stepanov

Authors
  1. G. Buttazzo
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  2. M. E. Drakhlin
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  3. L. Freddi
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  4. E. Stepanov
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Buttazzo, G., Drakhlin, M.E., Freddi, L. et al. Homogenization of Optimal Control Problems for Functional Differential Equations. Journal of Optimization Theory and Applications 93, 103–119 (1997). https://doi.org/10.1023/A:1022649817825

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  • DOI: https://doi.org/10.1023/A:1022649817825

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