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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 2, Pages 78–98 (Mi ufa246)  

This article is cited in 3 scientific papers (total in 3 papers)

On control of degenerate distributed systems

M. V. Plekhanovaa, V. E. Fedorovb

a South Ural State University, Chelyabinsk, Russia
b Chelyabinsk State University, Chelyabinsk, Russia

Abstract: We study the control of linear distributed control systems described by differential equations in Banach spaces with a degenerate operator at the derivative. A homogeneous part of equations has a degenerate strongly continuous resolving semigroup. For such system with generally speaking time-dependent bounded operator at the control function we find the criteria of the $\varepsilon$-control for time $T$ and of the $\varepsilon$-control in for a free time in terms of the operators involved in the equation. General results are used for studying of the $\varepsilon$-control of the considered systems with a finite-dimensional input. The obtained conditions are demonstrated by examples of control systems described by partial differential equations and systems of equations unsolved with respect to the time derivative.

Keywords: control system, degenerate evolution equation, Sobolev type equation, control.

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English version:
Ufa Mathematical Journal, 2014, 6:2, 77–96 (PDF, 464 kB); https://doi.org/10.13108/2014-6-2-77

UDC: 517.9
MSC: 93B05, 34G10, 47N70, 47F05
Received: 12.12.2013

Citation: M. V. Plekhanova, V. E. Fedorov, “On control of degenerate distributed systems”, Ufimsk. Mat. Zh., 6:2 (2014), 78–98; Ufa Math. J., 6:2 (2014), 77–96

Citation in format AMSBIB
\Bibitem{PleFed14}
\by M.~V.~Plekhanova, V.~E.~Fedorov
\paper On control of degenerate distributed systems
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 2
\pages 78--98
\mathnet{http://mi.mathnet.ru/ufa246}
\elib{http://elibrary.ru/item.asp?id=21596976}
\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 2
\pages 77--96
\crossref{https://doi.org/10.13108/2014-6-2-77}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928179121}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. E. Fedorov, D. M. Gordievskikh, G. D. Baybulatova, “Controllability of a Class of Weakly Degenerate Fractional Order Evolution Equations”, Proceedings of the 8Th International Conference on Mathematical Modeling, ICMM-2017, 1907, eds. I. Egorov, S. Popov, P. Vabishchevich, M. Antonov, N. Lazarev, M. Troeva, A. Ivanova A., et al., Amer. Inst. Physics, 2017, UNSP 020009  crossref  isi  scopus
    2. V. E. Fedorov, D. M. Gordievskikh, M. M. Turov, “Beskonechnomernaya i konechnomernaya $\varepsilon$-upravlyaemost odnogo klassa vyrozhdennykh evolyutsionnykh uravnenii drobnogo poryadka”, Chelyab. fiz.-matem. zhurn., 3:1 (2018), 5–26  mathnet  elib
    3. V. E. Fedorov, D. M. Gordievskikh, “Approximate controllability of strongly degenerate fractional order system of distributed control”, IFAC-PapersOnLine, 51:32 (2018), 675–680  crossref  isi  scopus
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