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
(F10F2F3−F∗1F5−F∗5F∗2−F4),
, 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.
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
\Bibitem{Kur01}
\by G.~A.~Kurina
\paper Invertibility of an Operator Appearing in the Control Theory for Linear Systems
\jour Mat. Zametki
\yr 2001
\vol 70
\issue 2
\pages 230--236
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\crossref{https://doi.org/10.4213/mzm736}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1882412}
\zmath{https://zbmath.org/?q=an:1045.93011}
\transl
\jour Math. Notes
\yr 2001
\vol 70
\issue 2
\pages 206--212
\crossref{https://doi.org/10.1023/A:1010254808822}
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Linking options:
https://www.mathnet.ru/eng/mzm736
https://doi.org/10.4213/mzm736
https://www.mathnet.ru/eng/mzm/v70/i2/p230
This publication is cited in the following 10 articles:
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
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
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
Qi Ya., Huang J., Chen A., “Spectral Inclusion Properties of Unbounded Hamiltonian Operators”, Chin. Ann. Math. Ser. B, 36:2 (2015), 201–212
Wu D., Chen A., “Invertibility of Nonnegative Hamiltonian Operator with Unbounded Entries”, J. Math. Anal. Appl., 373:2 (2011), 410–413
Alatancang, W, “Structure of the spectrum of infinite dimensional Hamiltonian operators”, Science in China Series A-Mathematics, 51:5 (2008), 915
Fedorov, VE, “Optimal control of Sobolev type linear equations”, Differential Equations, 40:11 (2004), 1627
Plekhanova, MV, “An optimal control problem for a class of degenerate equations”, Journal of Computer and Systems Sciences International, 43:5 (2004), 698
V. E. Fedorov, M. V. Plekhanova, “Optimal control of sobolev type linear equations”, Diff Equat, 40:11 (2004), 1627
V. E. Fedorov, M. V. Plekhanova, “Optimal control of sobolev type linear equations”, Diff Equat, 40:11 (2004), 1627