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Systems of control over set-valued trajectories with terminal quality criterion

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Ukrainian Mathematical Journal Aims and scope

We consider the optimal control problem with terminal quality criterion in which the state of a system is described by a set-valued mapping, and an admissible control is a summable function. We describe an algorithm that approximates the admissible control function by a piecewise-constant function and prove theorems on the closeness of the corresponding trajectories and the values of quality criteria.

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References

  1. M. Hukuhara, “Integration des applications mesurables dont la valeur est un compact convexe,” Funkc. Ekvacioj, No. 10, 205–223 (1967).

    Google Scholar 

  2. F. S. de Blasi and F. Iervolino, “Equazioni differenziali con soluzioni a valore compatto convesso,” Boll. Unione Mat. Ital., 2, No. 4–5, 491–501 (1969).

    MATH  Google Scholar 

  3. A. J. Brandao Lopes Pinto, F. S. de Blasi, and F. Iervolino, “Uniqueness and existence theorems for differential equations with compact convex valued solutions,” Boll. Unione Mat. Ital., No. 4, 534–538 (1970).

    Google Scholar 

  4. V. A. Plotnikov, A. V. Plotnikov, and A. N. Vityuk, Differential Equations with Multivalued Right-Hand Sides. Asymptotic Methods [in Russian], AstroPrint, Odessa (1999).

  5. M. Kisielewicz, “Method of averaging for differential equations with compact convex valued solutions,” Rend. Mat., 9, No. 3, 397–408 (1976).

    MATH  MathSciNet  Google Scholar 

  6. A. A. Tolstonogov, Differential Inclusions in a Banach Space [in Russian], Nauka, Novosibirsk (1986).

    MATH  Google Scholar 

  7. O. Kaleva, “Fuzzy differential equations,” Fuzzy Sets Syst., 24, No. 3, 301–317 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  8. O. Kaleva, “The Cauchy problem for fuzzy differential equations,” Fuzzy Sets Syst., 35, 389–396 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Celikovsky, “On the representation of trajectories of bilinear systems and its applications,” Kybernetika, 23, No. 3, 198–213 (1987).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Odessa National University, Odessa, Ukraine

    A. V. Arsirii

  2. Odessa State Academy of Civil Engineering and Architecture, Odessa, Ukraine

    A. V. Plotnikov

Authors
  1. A. V. Arsirii
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  2. A. V. Plotnikov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 8, pp. 1142 – 1147, August, 2009.

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Arsirii, A.V., Plotnikov, A.V. Systems of control over set-valued trajectories with terminal quality criterion. Ukr Math J 61, 1349–1356 (2009). https://doi.org/10.1007/s11253-010-0280-3

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  • DOI: https://doi.org/10.1007/s11253-010-0280-3

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