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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 2, Pages 222–237 (Mi vuu582)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On Hamilton–Jacobi–Isaacs–Bellman equation for neutral type systems

A. R. Plaksin

N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S.Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: For a conflict-controlled dynamical system described by functional differential equations of neutral type in Hales 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 HamiltonJacobi 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 HamiltonJacobi 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation -3047.2017.1


DOI: https://doi.org/10.20537/vm170206

Full text: PDF file (338 kB)
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Bibliographic databases:

Document Type: Article
UDC: 517.952, 517.977
MSC: 49L20, 49N70
Received: 17.03.2017

Citation: A. R. Plaksin, “On Hamilton–Jacobi–Isaacs–Bellman equation for neutral type systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017), 222–237

Citation in format AMSBIB
\Bibitem{Pla17}
\by A.~R.~Plaksin
\paper On Hamilton--Jacobi--Isaacs--Bellman equation for neutral type systems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 2
\pages 222--237
\mathnet{http://mi.mathnet.ru/vuu582}
\crossref{https://doi.org/10.20537/vm170206}
\elib{http://elibrary.ru/item.asp?id=29410193}


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    This publication is cited in the following articles:
    1. N. Yu. Lukoyanov, A. R. Plaksin, “Stable Functionals of Neutral-Type Dynamical Systems”, Proc. Steklov Inst. Math., 304 (2019), 205–218  mathnet  crossref  crossref  elib
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