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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 2, Pages 177–194 (Mi izv2662)  

This article is cited in 10 scientific papers (total in 10 papers)

On the existence and uniqueness of solutions of optimal control problems of linear distributed systems which are not solved with respect to the time derivative

M. V. Plekhanovaa, V. E. Fedorovb

a Chelyabinsk State Pedagogical University
b Chelyabinsk State University

Abstract: We investigate optimal control problems for linear distributed systems which are not solved with respect to the time derivative and whose homogeneous part admits a degenerate strongly continuous solution semigroup. To this end, we first obtain theorems on the existence of a unique strong solution of the Cauchy problem. This enables us to formulate sufficient conditions for the solubility of the optimal control problems under consideration. In contrast to earlier papers on a similar topic, we substantially weaken the conditions on the quality functional with respect to the state function. The abstract results thus obtained are illustrated by an example of an optimal control problem for the linearized system of Navier–Stokes equations.

Keywords: optimal control problem, distributed system, equation of Sobolev type, degenerate operator semigroup, unique solubility.

DOI: https://doi.org/10.4213/im2662

Full text: PDF file (578 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:2, 395–412

Bibliographic databases:

UDC: 517.97
MSC: Primary 49J20; Secondary 34H05, 35Q93, 49J15, 49K20, 93C20
Received: 10.05.2007
Revised: 20.05.2008

Citation: M. V. Plekhanova, V. E. Fedorov, “On the existence and uniqueness of solutions of optimal control problems of linear distributed systems which are not solved with respect to the time derivative”, Izv. RAN. Ser. Mat., 75:2 (2011), 177–194; Izv. Math., 75:2 (2011), 395–412

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Plekhanova, “Startovoe upravlenie vyrozhdennymi lineinymi raspredelennymi sistemami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:4 (2013), 53–68  mathnet  zmath  elib
    2. M. V. Plekhanova, “Sistemy optimalnosti dlya vyrozhdennykh raspredelennykh zadach upravleniya”, Vestnik ChelGU, 2013, no. 16, 60–70  mathnet  mathscinet  elib
    3. M. V. Plekhanova, V. E. Fedorov, “On control of degenerate distributed systems”, Ufa Math. J., 6:2 (2014), 77–96  mathnet  crossref  elib
    4. M. V. Plekhanova, G. D. Baibulatova, “Metod uslovnogo gradienta dlya odnoi zadachi zhestkogo upravleniya vyrozhdennoi evolyutsionnoi sistemoi”, Chelyab. fiz.-matem. zhurn., 1:1 (2016), 81–92  mathnet  elib
    5. M. V. Plekhanova, G. D. Baibulatova, “Chislennoe issledovanie zadachi zhestkogo upravleniya linearizovannoi kvazistatsionarnoi sistemoi uravnenii fazovogo polya”, Chelyab. fiz.-matem. zhurn., 1:2 (2016), 44–58  mathnet  elib
    6. A. F. Shuklina, M. V. Plekhanova, “Zadachi smeshannogo upravleniya dlya sistemy Soboleva”, Chelyab. fiz.-matem. zhurn., 1:2 (2016), 78–84  mathnet  elib
    7. M. V. Plekhanova, “Zadachi startovogo upravleniya dlya evolyutsionnykh uravnenii drobnogo poryadka”, Chelyab. fiz.-matem. zhurn., 1:3 (2016), 15–36  mathnet
    8. V. E. Fedorov, L. V. Borel, “Study of degenerate evolution equations with memory by operator semigroup methods”, Siberian Math. J., 57:4 (2016), 704–714  mathnet  crossref  crossref  isi  elib  elib
    9. Plekhanova M.V., “Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative”, Discret. Contin. Dyn. Syst.-Ser. S, 9:3 (2016), 833–846  crossref  mathscinet  zmath  isi  elib  scopus
    10. Fedorov V.E., Gordievskikh D.M., Baybulatova G.D., “Controllability of a Class of Weakly Degenerate Fractional Order Evolution Equations”, Proceedings of the 8th International Conference on Mathematical Modeling (ICMM-2017), AIP Conference Proceedings, 1907, eds. Egorov I., Popov S., Vabishchevich P., Antonov M., Lazarev N., Troeva M., Troeva M., Ivanova A., Gri, Amer Inst Physics, 2017, UNSP 020009  crossref  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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