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.
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
\Bibitem{Luk09}
\by N.~Yu.~Lukoyanov
\paper On optimality conditions for the guaranteed result in control problems for time-delay systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 3
\pages 158--169
\mathnet{http://mi.mathnet.ru/timm413}
\elib{https://elibrary.ru/item.asp?id=12834739}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 268
\issue , suppl. 1
\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:
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
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
Anton Plaksin, “Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems”, Appl Math Optim, 88:1 (2023)
Mikhail I. Gomoyunov, “On differentiability of solutions of fractional differential equations with respect to initial data”, Fract Calc Appl Anal, 25:4 (2022), 1484
N. Yu. Lukoyanov, A. R. Plaksin, “Quasigradient Aiming Strategies in Optimal Control Problems for Time-Delay Systems”, Diff Equat, 58:11 (2022), 1514
Anton Plaksin, “Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems”, J Optim Theory Appl, 187:1 (2020), 22
N. Yu. Lukoyanov, A. R. Plaksin, “Stable Functionals of Neutral-Type Dynamical Systems”, Proc. Steklov Inst. Math., 304 (2019), 205–218
Bayraktar E. Keller Ch., “Path-Dependent Hamilton–Jacobi Equations in Infinite Dimensions”, J. Funct. Anal., 275:8 (2018), 2096–2161
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
N. Yu. Lukoyanov, “On Hamilton–Jacobi formalism in time-delay control systems”, Tr. IMM UrO RAN, 16, no. 5, 2010, 269–277