Abstract:
A control system governed by a non-linear first-order
evolution equation with mixed non-convex control constraints
is examined. The system depends on parameters entering all
its data, including the non-linear evolution operator and
the control constraints. The system with convexified control
constraints is also considered. The general concept of $G$-convergence of operators is used for the proof of the existence of selectors continuously dependent on the parameters with
values in the solution set of the original system; a continuous version of the selector relaxation theorem is also proved, which concerns the approximation of the continuous solution selectors with convexified constraints by continuous solution selectors
of the original system. An example of a parabolic control system
is discussed.
\Bibitem{Tol03}
\by A.~A.~Tolstonogov
\paper On solutions of an~evolution control system depending on parameters
\jour Sb. Math.
\yr 2003
\vol 194
\issue 9
\pages 1383--1409
\mathnet{http://mi.mathnet.ru/eng/sm769}
\crossref{https://doi.org/10.1070/SM2003v194n09ABEH000769}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2037505}
\zmath{https://zbmath.org/?q=an:1113.93061}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000188170200005}
\elib{https://elibrary.ru/item.asp?id=13907791}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0742305832}
Linking options:
https://www.mathnet.ru/eng/sm769
https://doi.org/10.1070/SM2003v194n09ABEH000769
https://www.mathnet.ru/eng/sm/v194/i9/p113
This publication is cited in the following 9 articles:
I. V. Andrianov, A. G. Kolpakov, S. I. Rakin, “Justification of the Averaged Joule–Lenz Law for Composite Materials”, J Appl Mech Tech Phy, 2024
I. V. Andrianov, A. G. Kolpakov, S. I. Rakin, “Obosnovanie osrednennogo zakona Dzhoulya–Lentsa dlya kompozitsionnykh materialov”, Prikl. mekh. tekhn. fiz., 65:2 (2024), 138–145
Tolstonogov A.A., “Existence and relaxation of solutions for a subdifferential inclusion with unbounded perturbation”, J. Math. Anal. Appl., 447:1 (2017), 269–288
Timoshin S.A., “Control system with hysteresis and delay”, Syst. Control Lett., 91 (2016), 43–47
S.A.. Timoshin, “Variational Stability of Some Optimal Control Problems Describing Hysteresis Effects”, SIAM J. Control Optim, 52:4 (2014), 2348
Pavel Krejčí, A.A.. Tolstonogov, S.A.. Timoshin, “A control problem in phase transition modeling”, Nonlinear Differ. Equ. Appl, 2014
Liu Z.H., Migorski S., “Analysis and Control of Differential Inclusions With Anti-Periodic Conditions”, Proc. R. Soc. Edinb. Sect. A-Math., 144:3 (2014), 591–602
A.A. Tolstonogov, “Continuity in the parameter of the minimum value of an integral functional over the solutions of an evolution control system”, Nonlinear Analysis: Theory, Methods & Applications, 2012
A. A. Tolstonogov, “Control systems of subdifferential type depending on a parameter”, Izv. Math., 72:5 (2008), 985–1022
Citation in format AMSBIB
Contact us: