Existence of a Value and a Saddle Point in Positional Differential Games for Neutral-Type Systems

被引：10

作者：

Gomoyunov, M. I. ^{[1
,2
]}

Lukoyanov, N. Yu. ^{[1
,2
]}

Plaksin, A. R. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Krasovskii Inst Math & Mech, Ural Branch, Ekaterinburg 620990, Russia

[2] Ural Fed Univ, Ekaterinburg 620002, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2017年 / 299卷

基金：

俄罗斯科学基金会;

关键词：

neutral type systems; control theory; differential games;

D O I：

10.1134/S0081543817090061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 performance index that estimates the motion history realized up to the terminal time and includes an integral estimation of realizations of the players' controls. The game is formalized in the class of pure positional strategies. The main result is the proof of the existence of a value and a saddle point in this game.

引用

页码：37 / 48

页数：12

共 15 条

[1] [Anonymous], 1963, Differential-Difference Equations
[2] [Anonymous], 1970, Annali di Matematica Pura ed Applicata, DOI DOI 10.1007/BF02413530
[3] [Anonymous], 1988, Differential Equations with Discontinuous Righthand Sides
[4] Bellman R., 1967, Differential-Difference Equations
[5] Filippov A. F., 1985, DIFFERENTIAL EQUATIO
[6] Isaacs R, 1965, Differential Games
[7] Isaacs R., 1967, DIFFERENTIAL GAMES
[8] Krasovskii NN, 1985, Control of a Dynamical System
[9] Krasovskii NN., 1974, Positional Differential Games
[10] KRIAZHINSKII AV, 1978, DOKL AKAD NAUK SSSR+, V239, P779

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