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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 1, Pages 129–162 (Mi izv594)  

This article is cited in 8 scientific papers (total in 8 papers)

Relaxation in control systems of subdifferential type

A. A. Tolstonogov

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

Abstract: In a separable Hilbert space we consider a control system with evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. The constraint on the control is given by a multivalued function with non-convex values that is lower semicontinuous with respect to the variable states. Along with the original system we consider the system in which the constraint on the control is the upper semicontinuous convex-valued regularization of the original constraint. We study relations between the solution sets of these systems. As an application we consider a control variational inequality. We give an example of a control system of parabolic type with an obstacle.

DOI: https://doi.org/10.4213/im594

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English version:
Izvestiya: Mathematics, 2006, 70:1, 121–152

Bibliographic databases:

UDC: 517.988
Received: 01.12.2004

Citation: A. A. Tolstonogov, “Relaxation in control systems of subdifferential type”, Izv. RAN. Ser. Mat., 70:1 (2006), 129–162; Izv. Math., 70:1 (2006), 121–152

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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. Xiaoyou Liu, Zhenhai Liu, “Existence results for fractional semilinear differential inclusions in Banach spaces”, J. Appl. Math. Comput, 2012  crossref  mathscinet  scopus
    2. Xiaoyou Liu, Xi Fu, “Control Systems Described by a Class of Fractional Semilinear Evolution Equations and Their Relaxation Property”, Abstract and Applied Analysis, 2012 (2012), 1  crossref  mathscinet  zmath  isi  scopus
    3. Xiaoyou Liu, Zhenhai Liu, “Relaxation control for a class of evolution hemivariational inequalities”, Isr. J. Math, 2014  crossref  mathscinet  scopus
    4. A.A. Tolstonogov, “Sweeping process with unbounded nonconvex perturbation”, Nonlinear Analysis: Theory, Methods & Applications, 108 (2014), 291  crossref  mathscinet  zmath  scopus
    5. Liu X., Liu Zh., “On the ‘Bang-Bang’ Principle For a Class of Fractional Semilinear Evolution Inclusions”, Proc. R. Soc. Edinb. Sect. A-Math., 144:2 (2014), 333–349  crossref  mathscinet  zmath  isi  scopus
    6. Tolstonogov A.A., “Subdifferential inclusions with unbounded perturbation: Existence and relaxation theorems”, Dokl. Math., 94:1 (2016), 396–400  crossref  zmath  isi  elib  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  elib  scopus
    8. Li X., Liu Zh., “Relaxation in Nonconvex Optimal Control Problems For Nonautonomous Fractional Evolution Equations”, Pac. J. Optim., 13:3 (2017), 443–462  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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