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 ε-control for time T and of the ε-control in for a free time in terms of the operators involved in the equation. General results are used for studying of the ε-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.
\Bibitem{PleFed14}
\by M.~V.~Plekhanova, V.~E.~Fedorov
\paper On control of degenerate distributed systems
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 2
\pages 77--96
\mathnet{http://mi.mathnet.ru/eng/ufa246}
\crossref{https://doi.org/10.13108/2014-6-2-77}
\elib{https://elibrary.ru/item.asp?id=21596976}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928179121}
Linking options:
https://www.mathnet.ru/eng/ufa246
https://doi.org/10.13108/2014-6-2-77
https://www.mathnet.ru/eng/ufa/v6/i2/p78
This publication is cited in the following 7 articles:
Zhao D., Liu Ya., Li H., “Fast-Time Complete Controllability of Nonlinear Fractional Delay Integrodifferential Evolution Equations With Nonlocal Conditions and a Parameter”, Math. Meth. Appl. Sci., 45:10 (2022), 5649–5669
V E Fedorov, D M Gordievskikh, N V Filin, “On approximate controllability of a class of degenerate fractional order distributed systems”, J. Phys.: Conf. Ser., 1847:1 (2021), 012017
A. S. Avilovich, D. M. Gordievskikh, V. E. Fedorov, “Voprosy odnoznachnoi razreshimosti i priblizhennoi upravlyaemosti dlya lineinykh uravnenii drobnogo poryadka s gelderovoi pravoi chastyu”, Chelyab. fiz.-matem. zhurn., 5:1 (2020), 5–21
D. Baleanu, V. E. Fedorov, D. M. Gordievskikh, K. Tas, “Approximate controllability of infinite-dimensional degenerate fractional order systems in the sectorial case”, Mathematics, 7:8 (2019), 735
D. M. Gordievskikh, V. E. Fedorov, M. M. Turov, “Beskonechnomernaya i konechnomernaya ε-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
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
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