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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 3, Pages 158–169 (Mi timm413)  

This article is cited in 10 scientific papers (total in 10 papers)

On optimality conditions for the guaranteed result in control problems for time-delay systems

N. Yu. Lukoyanov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
References:
Abstract: For control problems under disturbance of dynamical systems described by differential equations with discrete and distributed time delays and with initial data satisfying the Lipschitz property, the corresponding Lipschitzness of the optimal guaranteed result functional is established and inequalities for its directional derivatives are obtained.
Keywords: optimal control, differential games, time-delay systems.
Received: 04.03.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 268, Issue 1, Pages S175–S187
DOI: https://doi.org/10.1134/S0081543810050135
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: N. Yu. Lukoyanov, “On optimality conditions for the guaranteed result in control problems for time-delay systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 158–169; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S175–S187
Citation in format AMSBIB
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\paper On optimality conditions for the guaranteed result in control problems for time-delay systems
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\vol 15
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\pages 158--169
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\vol 268
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\pages S175--S187
\crossref{https://doi.org/10.1134/S0081543810050135}
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Linking options:
  • https://www.mathnet.ru/eng/timm413
  • https://www.mathnet.ru/eng/timm/v15/i3/p158
  • This publication is cited in the following 10 articles:
    1. M. I. Gomoyunov, N. Yu. Lukoyanov, “Minimax solutions of Hamilton–Jacobi equations in dynamic optimization problems for hereditary systems”, Russian Math. Surveys, 79:2 (2024), 229–324  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. M.I. Gomoyunov, “On viscosity solutions of path-dependent Hamilton–Jacobi–Bellman–Isaacs equations for fractional-order systems”, Journal of Differential Equations, 399 (2024), 335  crossref
    3. Anton Plaksin, “Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems”, Appl Math Optim, 88:1 (2023)  crossref
    4. Mikhail I. Gomoyunov, “On differentiability of solutions of fractional differential equations with respect to initial data”, Fract Calc Appl Anal, 25:4 (2022), 1484  crossref
    5. N. Yu. Lukoyanov, A. R. Plaksin, “Quasigradient Aiming Strategies in Optimal Control Problems for Time-Delay Systems”, Diff Equat, 58:11 (2022), 1514  crossref
    6. Anton Plaksin, “Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems”, J Optim Theory Appl, 187:1 (2020), 22  crossref
    7. N. Yu. Lukoyanov, A. R. Plaksin, “Stable Functionals of Neutral-Type Dynamical Systems”, Proc. Steklov Inst. Math., 304 (2019), 205–218  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Bayraktar E. Keller Ch., “Path-Dependent Hamilton–Jacobi Equations in Infinite Dimensions”, J. Funct. Anal., 275:8 (2018), 2096–2161  crossref  mathscinet  zmath  isi  scopus
    9. A. R. Plaksin, “Ob uravnenii Gamiltona–Yakobi–Aizeksa–Bellmana dlya sistem neitralnogo tipa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 222–237  mathnet  crossref  elib
    10. N. Yu. Lukoyanov, “On Hamilton–Jacobi formalism in time-delay control systems”, Tr. IMM UrO RAN, 16, no. 5, 2010, 269–277  mathnet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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