Email this article Minimax differential game with delay
- Authors: Kim A.V.1, Bocharov G.A.2
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Affiliations:
- N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
- Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences
- Issue: Vol 25, No 132 (2020)
- Pages: 359-369
- Section: Articles
- URL: https://journal-vniispk.ru/2686-9667/article/view/294974
- DOI: https://doi.org/10.20310/2686-9667-2020-25-132-359-369
- ID: 294974
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Abstract
The paper considers a minimax positional differential game with aftereffect based on the i -smooth analysis methodology. In the finite-dimensional (ODE) case for a minimax differential game, resolving mixed strategies can be constructed using the dynamic programming method. The report shows that the i -smooth analysis methodology allows one to construct counterstrategies in a completely similar way to the finite-dimensional case. Moreover as it is typical for the use of i -smooth analysis, in the absence of an aftereffect, all the results of the article pass to the corresponding results of the finite-dimensional theory of positional differential games.
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About the authors
Arkadii V. Kim
N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
Email: avkim@imm.uran.ru
Doctor of Physics and Mathematics, Senior Scientific Researcher 16 S. Kovalevskaya St., Yekaterinburg 620108, Russian Federation
Gennady A. Bocharov
Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences
Email: bocharov@inm.ras
Doctor of Physics and Mathematics, Leading Scientific Researcher 8 Gubkin St., Moscow 119333, Russian Federation
References
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- N. A. Andryushechkina, A. V. Ivanov, A. V. Kim, "Application of i-Smooth Analysis to Differential Games with Delays", Control Applications of Optimization, Proceedings of the 17th IFAC Workshop (Yekaterinburg, Russia, October 15-19, 2018), Krasovskii Inst. of Mathematics and Mechanics, UB of RAS, Yekaterinburg, 2018, 19e.
- A. V. Kim, i-Smooth Analysis. Theory and Applications, Wiley, New Jersey, 2015.
- A. V. Kim, A. V. Ivanov, Systems with Delays. Analysis, Control, Computations, Wiley, New Jersey, 2015.
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