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Avtomat. i Telemekh., 2011, Issue 3, Pages 36–50 (Mi at1488)  

This article is cited in 18 scientific papers (total in 18 papers)

Nonlinear Systems

Degenerate problems of optimal control. I

V. I. Gurmana, Ni Ming Kangb

a Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalesskii, Russia
b East China Normal University, Shanghai, China

Abstract: Considered is the practically important and theoretically challenging class of optimal control problems which can be integrated within the common notion of “degenerate problems”. The general definition of such problems is given, which arises from the connection between the degeneracy and the presence of hidden passive differential constraints or discrete chains in the problem. This definition is analyzed with the focus on its relation with the classical notion of degeneracy in the variational calculus and the notion of singular and sliding modes well known in the control theory. This paper is the first one in the series of three, which are aimed at presenting a survey of the main facts and applications of the special theory of such problems, which is essentially based on finding and eliminating passive constraints. New results and generalizations are also reported.

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English version:
Automation and Remote Control, 2011, 72:3, 497–511

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Presented by the member of Editorial Board: Е. Я. Рубинович

Received: 18.03.2010

Citation: V. I. Gurman, Ni Ming Kang, “Degenerate problems of optimal control. I”, Avtomat. i Telemekh., 2011, no. 3, 36–50; Autom. Remote Control, 72:3 (2011), 497–511

Citation in format AMSBIB
\by V.~I.~Gurman, Ni~Ming~Kang
\paper Degenerate problems of optimal control.~I
\jour Avtomat. i Telemekh.
\yr 2011
\issue 3
\pages 36--50
\jour Autom. Remote Control
\yr 2011
\vol 72
\issue 3
\pages 497--511

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    This publication is cited in the following articles:
    1. V. I. Gurman, Ni Ming Kang, “Degenerate problems of optimal control. II”, Autom. Remote Control, 72:4 (2011), 727–739  mathnet  crossref  mathscinet  zmath  isi
    2. V. I. Gurman, Ni Ming Kang, “Degenerate problems of optimal control. III”, Autom. Remote Control, 72:5 (2011), 929–943  mathnet  crossref  mathscinet  zmath  isi
    3. V. I. Gurman, I. V. Rasina, “Control improvement and approximately optimal synthesis in the neighborhood of a support trajectory”, Autom. Remote Control, 72:12 (2011), 2445–2457  mathnet  crossref  mathscinet  zmath  isi
    4. V. I. Gurman, I. V. Rasina, “Discrete-continuous representations of impulsive processes in the controllable systems”, Autom. Remote Control, 73:8 (2012), 1290–1300  mathnet  crossref  isi
    5. I. V. Rasina, “Degenerate problems of optimal control for discrete-continuous (hybrid) systems”, Autom. Remote Control, 74:2 (2013), 196–206  mathnet  crossref  zmath  isi
    6. V. I. Gurman, I. V. Rasina, O. V. Fesko, “O prakticheskikh preobrazovaniyakh vyrozhdennykh zadach optimalnogo upravleniya”, Programmnye sistemy: teoriya i prilozheniya, 4:2 (2013), 71–82  mathnet
    7. V. I. Gurman, “On transformations of degenerate optimal control problems”, Autom. Remote Control, 74:11 (2013), 1878–1882  mathnet  crossref  isi
    8. V. I. Gurman, I. S. Guseva, “Modeli upravlyaemykh sistem, porozhdayuschie magistralnye resheniya zadach optimalnogo upravleniya”, Programmnye sistemy: teoriya i prilozheniya, 4:4 (2013), 107–125  mathnet
    9. V. I. Gurman, O. V. Fesko, I. S. Guseva, S. N. Nasatueva, “Iteratsionnye protsedury na osnove metoda globalnogo uluchsheniya upravleniya”, Programmnye sistemy: teoriya i prilozheniya, 5:2 (2014), 47–61  mathnet
    10. V. I. Gurman, I. V. Rasina, “Optimization of processes in a spin chain”, Autom. Remote Control, 75:12 (2014), 2212–2216  mathnet  crossref  isi
    11. I. V. Rasina, O. V. Baturina, “Lineino-kvadraticheskie diskretno-nepreryvnye sistemy s upravlyaemymi koeffitsientami”, Programmnye sistemy: teoriya i prilozheniya, 6:1 (2015), 21–37  mathnet
    12. V. I. Gurman, I. V. Rasina, “Turnpike solutions in the problem of excitation transfer along a spin chain”, Programmnye sistemy: teoriya i prilozheniya, 7:1 (2016), 3–13  mathnet
    13. V. I. Gurman, I. V. Rasina, O. V. Fes'ko, I. S. Guseva, “On certain approaches to optimization of control processes. I”, Autom. Remote Control, 77:8 (2016), 1370–1385  mathnet  crossref  isi  elib  elib
    14. V. I. Gurman, I. V. Rasina, O. V. Fesko, I. S. Guseva, “On certain approaches to optimization of control processes. II”, Autom. Remote Control, 77:9 (2016), 1544–1556  mathnet  crossref  isi  elib
    15. V. I. Gurman, M. M. Khrustalev, “Anormalnost v teorii neobkhodimykh uslovii optimalnosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 44–61  mathnet  crossref
    16. I. V. Rasina, O. V. Fesko, “Vyrozhdennye zadachi optimalnogo upravleniya neodnorodnymi diskretnymi sistemami”, Programmnye sistemy: teoriya i prilozheniya, 8:2 (2017), 3–18  mathnet  crossref
    17. A. V. Zarodnyuk, D. I. Bugrov, O. Yu. Cherkasov, “O svoistvakh reaktsii opornoi krivoi v zadache o maksimizatsii dalnosti v soprotivlyayuscheisya srede”, Fundament. i prikl. matem., 22:2 (2018), 147–158  mathnet
    18. Zarodnyuk A., Cherkasov O., “Support Reaction in the Brachistochrone Problem in a Resistant Medium”, Dynamical Systems in Applications, Springer Proceedings in Mathematics & Statistics, 249, ed. Awrejcewicz J., Springer International Publishing Ag, 2018, 451–460  crossref  isi  scopus
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