Abstract:
For a linear dynamical system with control and disturbance, a feedback control problem is considered, in which the Euclidean norm of a set of deviations of the system's motion from given targets at given instants of time is optimized. The problem is formalized into a differential game in “strategy-counter strategy” classes. A game value computing procedure which reduces the problem to a recursive construction of upper convex hulls of auxiliary functions is justified. Results of numerical simulations are presented.
Keywords:
Differential games, Value of the game, Saddle point, Counter strategies.
This work was supported by Complex Program of Fundamental Research UrO RAN (project 15-16-1-13).
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Mikhail I. Gomoyunov, Dmitry V. Kornev, “On calculating the value of a differential game in the class of counter strategies”, Ural Math. J., 2:1 (2016), 38–47
\Bibitem{GomKor16}
\by Mikhail~I.~Gomoyunov, Dmitry~V.~Kornev
\paper On calculating the value of a differential game in the class of counter strategies
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 1
\pages 38--47
\mathnet{http://mi.mathnet.ru/umj13}
\crossref{https://doi.org/10.15826/umj.2016.1.004}
\zmath{https://zbmath.org/?q=an:1398.91087}
\elib{https://elibrary.ru/item.asp?id=26501481}
This publication is cited in the following 4 articles:
Nikolai Lukoyanov, Mikhail Gomoyunov, “Differential Games on Minmax of the Positional Quality Index”, Dyn Games Appl, 9:3 (2019), 780
Mikhail Gomoyunov, Dmitriy Serkov, “On a Solution of a Guarantee Optimization Problem Under the Functional Constraints on the Disturbance”, Dyn Games Appl, 9:3 (2019), 700
N.Yu. Lukoyanov, M.I. Gomoyunov, “Traversing Target Points Under Lack of Information: A Game-Theoretical Approach”, IFAC-PapersOnLine, 51:32 (2018), 262
M.I. Gomoyunov, V.O. Karandina, I.P. Mezentsev, D.A. Serkov, “On the Stability of a Solution of a Guarantee Optimization Problem under a Functional Constraint on the Disturbance”, IFAC-PapersOnLine, 51:32 (2018), 228
Citation in format AMSBIB
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