 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| M.I. Gomoyunov and A.R. Plaksin, "On Basic Equation of Differential Games for Neutral-Type Systems," Mech. Solids. 54 (2), 131-143 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
2 |
Pages |
131-143 |
| DOI |
10.3103/S0025654419030099 |
| Title |
On Basic Equation of Differential Games for Neutral-Type Systems |
| Author(s) |
M.I. Gomoyunov (Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 Russia; President B.N. Yeltsin Ural Federal University, Yekaterinburg, 620002 Russia, m.i.gomoyunov@gmail.com)
A.R. Plaksin (Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 Russia; President B.N. Yeltsin Ural Federal University, Yekaterinburg, 620002 Russia, a.r.plaksin@gmail.com) |
| Abstract |
For a conflict-controlled dynamical system described by neutral-type functional differential equations in Hale’s form, a differential game is considered in the classes of control strategies with a guide for a minimax-maximin of the quality index, which evaluates the system’s motion history implemented by the terminal time moment. The differential game is associated with the Cauchy problem for a functional Hamilton–Jacobi type equation in coinvariant derivatives. It has been proven that the game value functional coincides with the minimax solution of this problem. A method of constructing the optimal strategies of players is given. The approximation by ordinary Hamilton–Jacobi equations in partial derivatives is proposed for this functional Hamilton–Jacobi equation in coinvariant derivatives. |
| Keywords |
differential game, neutral-type equations, coinvariant derivatives, Hamilton–Jacobi equation, minimax solution, control with a guide, optimal strategies |
| Received |
26 July 2018 |
| Link to Fulltext |
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