Abstract:
For a dynamical system whose motion is described by neutral-type differential equations in Hale's form, we consider a minimax–maximin differential game with a quality index evaluating the motion history realized up to the terminal time. The control actions of the players are subject to geometric constraints. The game is formalized in classes of pure positional strategies with a memory of the motion history. It is proved that the game has a value and a saddle point. The proof is based on the choice of an appropriate Lyapunov–Krasovskii functional for the construction of control strategies by the method of an extremal shift to accompanying points.
Keywords:
neutral-type systems, control theory, differential games.
Citation:
N. Yu. Lukoyanov, A. R. Plaksin, “On the Theory of Positional Differential Games for Neutral-Type Systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 118–128; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S83–S92
\Bibitem{LukPla19}
\by N.~Yu.~Lukoyanov, A.~R.~Plaksin
\paper On the Theory of Positional Differential Games for Neutral-Type Systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 3
\pages 118--128
\mathnet{http://mi.mathnet.ru/timm1652}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-3-118-128}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2020
\vol 309
\issue , suppl. 1
\pages S83--S92
\crossref{https://doi.org/10.1134/S0081543820040100}
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Linking options:
https://www.mathnet.ru/eng/timm1652
https://www.mathnet.ru/eng/timm/v25/i3/p118
This publication is cited in the following 8 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
Anton Plaksin, “Optimal Positional Strategies in Differential Games for Neutral-Type Systems”, Dyn Games Appl, 2024
M. I. Gomoyunov, N. Yu. Lukoyanov, “Tsena i optimalnye strategii v pozitsionnoi differentsialnoi igre dlya sistemy neitralnogo tipa”, Tr. IMM UrO RAN, 30, no. 3, 2024, 86–98
A. V. Kim, “Vvedenie v teoriyu pozitsionnykh differentsialnykh igr sistem s posledeistviem (na osnove metodologii i-gladkogo analiza”, Vestnik rossiiskikh universitetov. Matematika, 29:147 (2024), 268–295
M. I. Gomoyunov, N. Yu. Lukoyanov, “The Value and Optimal Strategies in a Positional Differential Game for a Neutral-Type System”, Proc. Steklov Inst. Math., 327:S1 (2024), S112
Anton Plaksin, “Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems”, Appl Math Optim, 88:1 (2023)
E. M. Mukhsinov, “About one differential game of neutral type with integral restrictions in Hilbert space”, Ufa Math. J., 14:3 (2022), 86–96
A. R. Plaksin, “On the minimax solution of the Hamilton-Jacobi equations for neutral-type systems: the case of an inhomogeneous Hamiltonian”, Differ. Equ., 57:11 (2021), 1516–1526
Citation in format AMSBIB
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