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
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.
control system, degenerate evolution equation, Sobolev type equation, control.
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Ufa Mathematical Journal, 2014, 6:2, 77–96 (PDF, 464 kB); https://doi.org/10.13108/2014-6-2-77
MSC: 93B05, 34G10, 47N70, 47F05
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
\by M.~V.~Plekhanova, V.~E.~Fedorov
\paper On control of degenerate distributed systems
\jour Ufimsk. Mat. Zh.
\jour Ufa Math. J.
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This publication is cited in the following articles:
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
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
V. E. Fedorov, D. M. Gordievskikh, “Approximate controllability of strongly degenerate fractional order system of distributed control”, IFAC-PapersOnLine, 51:32 (2018), 675–680
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