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Ukrainian Mathematical Journal

, Volume 54, Issue 12, pp 2067–2074 | Cite as

Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem

  • O. A. Kapustyan
Article

Abstract

We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. In view of this fact, we justify the convergence of approximate controls, switching points, and values of the quality criterion to the exact values of the corresponding variables.

Keywords

Fourier Series Quality Criterion Laplace Operator Bound Control Switching Point 
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REFERENCES

  1. 1.
    J. L. Lions, Contróle Optimal de Systémes Gouvernés par des Équations aux Dérivées Partielles, Dunod Gauthier-Villars, Paris (1968).Google Scholar
  2. 2.
    A. I. Egorov, Optimal Control of Heat and Diffusion Processes [in Russian], Nauka, Moscow (1978).Google Scholar
  3. 3.
    E. A. Kapustyan and A. G. Nakonechnyi, “Synthesis of optimal bounded control for parabolic boundary-value problem with rapidly oscillating coefficients,” Probl. Upravl. Informatiki, No. 6, 44–57 (1999).Google Scholar
  4. 4.
    S. T. Zavalishchin, “Minimax variant of the Mayer problem for instantaneous restrictions on complete impulses of controls,” Tr. Inst. Mat. Mekh. Ural. Nauch. Tsentr. Akad. Nauk SSSR, 32, 34–44 (1979).Google Scholar
  5. 5.
    O. A. Ladyzhenskaya, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • O. A. Kapustyan
    • 1
  1. 1.Kiev UniversityKiev

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