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Matematicheskie Zametki, 2001, Volume 70, Issue 2, Pages 230–236
DOI: https://doi.org/10.4213/mzm736 (Mi mzm736) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Invertibility of an Operator Appearing in the Control Theory for Linear Systems

G. A. Kurina

Voronezh State Academy of Forestry Engineering
Full-text PDF (165 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm736
Abstract: We give sufficient conditions for the existence of a bounded inverse operator for a linear operator appearing in the theory of optimal control of linear systems in Hilbert space and having a matrix representation of the form
$$ \begin {pmatrix} F_1&0&F_2 \\F_3&-F_1^*&F_5 \\-F_5^*&F_2^*&-F_4 \end{pmatrix} , $$
, where $F3$, $F4$ are nonnegative self-adjoint operators. The invertibility of the operator under study is used to prove the unique solvability of a certain two-point boundary-value problem that arises from conditions for optimal control.
Received: 03.04.2000
English version:
Mathematical Notes, 2001, Volume 70, Issue 2, Pages 206–212
DOI: https://doi.org/10.1023/A:1010254808822
Bibliographic databases:
UDC: 517.983.24
Language: Russian
Citation: G. A. Kurina, “Invertibility of an Operator Appearing in the Control Theory for Linear Systems”, Mat. Zametki, 70:2 (2001), 230–236; Math. Notes, 70:2 (2001), 206–212
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    1. E. G. Krushel, E. S. Potafeeva, T. P. Ogar, I. V. Stepanchenko, I. M. Kharitonov, Studies in Systems, Decision and Control, 418, Cyber-Physical Systems: Modelling and Industrial Application, 2022, 161  crossref
    2. Liu J., Huang J., Chen A., “Symmetry of Numerical Range and Semigroup Generation of Infinite Dimensional Hamiltonian Operators”, Turk. J. Math., 42:1 (2018), 49–56  crossref  mathscinet  isi  scopus  scopus
    3. 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
    4. Qi Ya., Huang J., Chen A., “Spectral Inclusion Properties of Unbounded Hamiltonian Operators”, Chin. Ann. Math. Ser. B, 36:2 (2015), 201–212  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Wu D., Chen A., “Invertibility of Nonnegative Hamiltonian Operator with Unbounded Entries”, J. Math. Anal. Appl., 373:2 (2011), 410–413  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Alatancang, W, “Structure of the spectrum of infinite dimensional Hamiltonian operators”, Science in China Series A-Mathematics, 51:5 (2008), 915  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Fedorov, VE, “Optimal control of Sobolev type linear equations”, Differential Equations, 40:11 (2004), 1627  mathnet  crossref  mathscinet  zmath  isi
    8. Plekhanova, MV, “An optimal control problem for a class of degenerate equations”, Journal of Computer and Systems Sciences International, 43:5 (2004), 698  mathscinet  isi
    9. V. E. Fedorov, M. V. Plekhanova, “Optimal control of sobolev type linear equations”, Diff Equat, 40:11 (2004), 1627  crossref
    10. V. E. Fedorov, M. V. Plekhanova, “Optimal control of sobolev type linear equations”, Diff Equat, 40:11 (2004), 1627  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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