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 Tr. Semim. im. I. G. Petrovskogo, 2016, Issue 31, Pages 134–157 (Mi tsp93)

Some problems of distributed and boundary control for systems with integral aftereffect

I. V. Romanova, A. S. Shamaevbc

a National Research University "Higher School of Economics" (HSE), Moscow
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
c Lomonosov Moscow State University

Abstract: We consider the problem of exact control for a system described by an equation with integral “memory.” It is shown that, under certain conditions, this system can be brought to rest in finite time by distributed control bounded in absolute value, and, in a special one-dimensional case, by control applied to an end-point of the interval. We consider different types of kernels in the integral term of the equation and describe some relationships between problems of controllability of some hyperbolic and parabolic systems.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00412_à

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English version:
Journal of Mathematical Sciences (New York), 2018, 234:4, 470–484

UDC: 517.958

Citation: I. V. Romanov, A. S. Shamaev, “Some problems of distributed and boundary control for systems with integral aftereffect”, Tr. Semim. im. I. G. Petrovskogo, 31, 2016, 134–157; J. Math. Sci. (N. Y.), 234:4 (2018), 470–484

Citation in format AMSBIB
\Bibitem{RomSha16} \by I.~V.~Romanov, A.~S.~Shamaev \paper Some problems of distributed and boundary control for systems with integral aftereffect \serial Tr. Semim. im. I. G. Petrovskogo \yr 2016 \vol 31 \pages 134--157 \mathnet{http://mi.mathnet.ru/tsp93} \transl \jour J. Math. Sci. (N. Y.) \yr 2018 \vol 234 \issue 4 \pages 470--484 \crossref{https://doi.org/10.1007/s10958-018-4023-6} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052870311}