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Optimal Control of a Conditionally Correct System Described by a Quartic Equation with Conjugation Conditions

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Abstract

New optimal control problems for a conditionally correct system whose state is described by an elliptic quartic equation with conjugation conditions are considered. Efficient computation schemes for numerical determination of optimal controls are constructed, the admissible control sets being complete Hilbert spaces.

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REFERENCES

  1. I. V. Sergienko and V. S. Deineka, “Computational algorithms for a conditionally correct problem of deflections of a composite beam,” Dop. NANU, No. 7, 77–82 (2002).

    Google Scholar 

  2. E. F. Galba, “Weighted pseudoinversion and conditionally correct elliptic boundary-value problems in mathematical simulation: Theory, mathematical models, compulational methods,” Author’s Abstracts of PhD Thesis, V. M. Glushkov Inst. of Cybernetics, NAN Ukraine, Kiev (2001).

    Google Scholar 

  3. I. V. Sergienko and V. S. Deineka, “Optimal control of a conditionally correct system with conjugation conditions,” Kibern. Sist. Analiz, No. 4, 44–62 (2002).

  4. I. V. Sergienko and V. S. Deineka, “Optimal control of a system described by a two-dimensional quartic equation with conjugation conditions,” Kibern. Sist. Analiz, No. 2, 112–133 (2003).

  5. O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  6. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  7. V. S. Deineka and I. V. Sergienko, Models and Methods of Solving Problems in Inhomogeneous Media [in Russian], Naukova Dumka, Kiev (2001).

    Google Scholar 

  8. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam (1978).

    Google Scholar 

  9. J.-L. Lions, Optimal Control of the Systems Governed by Partial Differential Equations, Springer-Verag, Berlin (1971).

    Google Scholar 

  10. I. V. Sergienko and V. S. Deineka, “The Dirichlet and Neumann problems for elliptical equations with conjugation conditions and high-precision algorithms of their discretization,” Kibern. Sist. Analiz, No. 3, 35–62 (2001).

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The study was sponsored by the State Fund for Fundamental Research of the Ministry of Education and Science of Ukraine (contract No. F7/276-2001).

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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 156–174, January–February 2005.

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Sergienko, I.V., Deineka, V.S. Optimal Control of a Conditionally Correct System Described by a Quartic Equation with Conjugation Conditions. Cybern Syst Anal 41, 126–143 (2005). https://doi.org/10.1007/s10559-005-0047-2

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  • DOI: https://doi.org/10.1007/s10559-005-0047-2

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