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Home » Issues » Archive of Issues » 2017 - 2 issue » pp. 222-237

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Russia Yekaterinburg
Year
2017
Volume
27
Issue
2
Pages
222-237
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Section Mathematics
Title On Hamilton-Jacobi-Isaacs-Bellman equation for neutral type systems
Author(-s) Plaksin A.R.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
Abstract For a conflict-controlled dynamical system described by functional differential equations of neutral type in Hale’s form, we consider a differential game with a quality index that estimates the motion history realized up to the terminal time and includes an integral estimation of realizations of players’ controls. The game is formalized in the class of pure positional strategies. Based on a coinvariant derivatives conception we derive a Hamilton–Jacobi functional equation. It is proved, firstly, that the solution of this equation, satisfying certain conditions of smoothness, is the value of the initial differential game, and secondly, that value at points of differentiability satisfies the considered Hamilton–Jacobi equation. Thus this equation can be interpreted as the Hamilton-Jacobi-Isaacs-Bellman equation for neutral type systems.
Keywords neutral type systems, differential games, Hamilton-Jacobi equation
UDC 517.952, 517.977
MSC 49L20, 49N70
DOI 10.20537/vm170206
Received 17 March 2017
Language Russian
Citation Plaksin A.R. On Hamilton-Jacobi-Isaacs-Bellman equation for neutral type systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 2, pp. 222-237.
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