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Avtomat. i Telemekh., 2011, Issue 3, Pages 36–50
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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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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
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V. I. Gurman, Ni Ming Kang, “Degenerate problems of optimal control. II”, Autom. Remote Control, 72:4 (2011), 727–739
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V. I. Gurman, Ni Ming Kang, “Degenerate problems of optimal control. III”, Autom. Remote Control, 72:5 (2011), 929–943
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V. I. Gurman, I. V. Rasina, “Discrete-continuous representations of impulsive processes in the controllable systems”, Autom. Remote Control, 73:8 (2012), 1290–1300
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I. V. Rasina, “Degenerate problems of optimal control for discrete-continuous (hybrid) systems”, Autom. Remote Control, 74:2 (2013), 196–206
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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
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V. I. Gurman, “On transformations of degenerate optimal control problems”, Autom. Remote Control, 74:11 (2013), 1878–1882
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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
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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
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V. I. Gurman, I. V. Rasina, “Optimization of processes in a spin chain”, Autom. Remote Control, 75:12 (2014), 2212–2216
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I. V. Rasina, O. V. Baturina, “Lineino-kvadraticheskie diskretno-nepreryvnye sistemy s upravlyaemymi koeffitsientami”, Programmnye sistemy: teoriya i prilozheniya, 6:1 (2015), 21–37
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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
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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
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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
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V. I. Gurman, M. M. Khrustalev, “Anormalnost v teorii neobkhodimykh uslovii optimalnosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 44–61
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I. V. Rasina, O. V. Fesko, “Vyrozhdennye zadachi optimalnogo upravleniya neodnorodnymi diskretnymi sistemami”, Programmnye sistemy: teoriya i prilozheniya, 8:2 (2017), 3–18
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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
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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
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