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Mat. Sb., 2003, Volume 194, Number 9, Pages 113–140 (Mi msb769)  

This article is cited in 7 scientific papers (total in 7 papers)

On solutions of an evolution control system depending on parameters

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/sm769

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English version:
Sbornik: Mathematics, 2003, 194:9, 1383–1409

Bibliographic databases:

UDC: 517.97
MSC: Primary 93C20; Secondary 54C60, 54C65
Received: 28.05.2002 and 20.05.2003

Citation: A. A. Tolstonogov, “On solutions of an evolution control system depending on parameters”, Mat. Sb., 194:9 (2003), 113–140; Sb. Math., 194:9 (2003), 1383–1409

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v194/i9/p113

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Tolstonogov, “Control systems of subdifferential type depending on a parameter”, Izv. Math., 72:5 (2008), 985–1022  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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  crossref  mathscinet  isi  scopus
    3. S.A.. Timoshin, “Variational Stability of Some Optimal Control Problems Describing Hysteresis Effects”, SIAM J. Control Optim, 52:4 (2014), 2348  crossref  mathscinet  zmath  scopus
    4. Pavel Krejčí, A.A.. Tolstonogov, S.A.. Timoshin, “A control problem in phase transition modeling”, Nonlinear Differ. Equ. Appl, 2014  crossref  mathscinet  scopus
    5. 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  crossref  mathscinet  zmath  isi  elib  scopus
    6. Timoshin S.A., “Control system with hysteresis and delay”, Syst. Control Lett., 91 (2016), 43–47  crossref  mathscinet  zmath  isi  scopus
    7. Tolstonogov A.A., “Existence and relaxation of solutions for a subdifferential inclusion with unbounded perturbation”, J. Math. Anal. Appl., 447:1 (2017), 269–288  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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