Abstract:
A positional differential time-optimal game is considered for a conflict-controlled time-delay object. Minimax and maximin feedback controls are constructed within a scheme that includes an intermediate model object described by an ordinary differential equation and a stochastic guide described by the Ito differential equation. The motion of the guide is based on the real-time solution of a sequence of auxiliary boundary value problems for a parabolic equation with degenerate diffusion term.
Keywords:
time-delay object, minimax-maximin time of rendezvous, stochastic guide.
Citation:
N. N. Krasovskii, A. N. Kotel'nikova, “Stochastic guide for a time-delay object in a positional differential game”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 97–104; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 145–151
\Bibitem{KraKot11}
\by N.~N.~Krasovskii, A.~N.~Kotel'nikova
\paper Stochastic guide for a~time-delay object in a~positional differential game
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 2
\pages 97--104
\mathnet{http://mi.mathnet.ru/timm700}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2012
\vol 277
\issue , suppl. 1
\pages 145--151
\crossref{https://doi.org/10.1134/S0081543812050148}
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Linking options:
https://www.mathnet.ru/eng/timm700
https://www.mathnet.ru/eng/timm/v17/i2/p97
This publication is cited in the following 17 articles:
D. V. Khlopin, “A Differential Game with the Possibility of Early Termination”, Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S140–S164
M. I. Gomoyunov, N. Yu. Lukoyanov, “Construction of Solutions to Control Problems for Fractional-Order Linear Systems Based on Approximation Models”, Proc. Steklov Inst. Math. (Suppl.), 313, suppl. 1 (2021), S73–S82
Gomoyunov M., “Solution to a Zero-Sum Differential Game With Fractional Dynamics Via Approximations”, Dyn. Games Appl., 10:2 (2020), 417–443
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L. A. Vlasenko, A. G. Rutkas, A. A. Chikrii, “On a Differential Game in a Stochastic System”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S185–S198
Gomoyunov M.I., “Fractional Derivatives of Convex Lyapunov Functions and Control Problems in Fractional Order Systems”, Fract. Calc. Appl. Anal., 21:5 (2018), 1238–1261
Plaksin A.R., “Approximation of Linear Conflict-Controlled Neutral-Type Systems”, IFAC PAPERSONLINE, 51:32 (2018), 256–261
Yu. Averboukh, “Extremal Shift Rule For Continuous-Time Zero-Sum Markov Games”, Dyn. Games Appl., 7:1 (2017), 1–20
M. I. Gomoyunov, A. R. Plaksin, “Konechnomernye approksimatsii konfliktno-upravlyaemykh sistem neitralnogo tipa”, Izv. IMI UdGU, 49 (2017), 111–122
M. Gomoyunov, A. Plaksin, “Finite-Dimensional Approximations of Neutral-Type Conflict-Controlled Systems”, IFAC-PapersOnLine, 50:1 (2017), 5109–5114
Yu. Averboukh, “Approximate Solutions of Continuous-Time Stochastic Games”, SIAM J. Control Optim., 54:5 (2016), 2629–2649
Dmitry V. Khlopin, “Uniform Tauberian theorem in differential games”, Autom. Remote Control, 77:4 (2016), 734–750
V. S. Kublanov, V. I. Maksimov, “On feedback-principle control for systems with aftereffect under incomplete phase-coordinate data”, Journal of Mathematical Sciences, 233:4 (2018), 495–513
A. R. Plaksin, “Finite-Dimensional Guides For Conflict-Controlled Linear Systems of Neutral Type”, Differ. Equ., 51:3 (2015), 406–416
“Nikolai Nikolaevich Krasovskii (on the occasion of his 90th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 1–21
N. Yu. Lukoyanov, A. R. Plaksin, “On the approximation of nonlinear conflict-controlled systems of neutral type”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 182–196
N. Yu. Lukoyanov, A. R. Plaksin, “Konechnomernye modeliruyuschie povodyri v sistemakh s zapazdyvaniem”, Tr. IMM UrO RAN, 19, no. 1, 2013, 182–195
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