The solution set of the N-player scalar feedback Nash algebraic Riccati equations

被引：7

作者：

Engwerda, JC ^{[1
]}

机构：

[1] Tilburg Univ, Dept Econometr, NL-5000 LE Tilburg, Netherlands

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2000年 / 45卷 / 12期

关键词：

algebraic Ricati equations; differential games; feedback Nash equilibrium; linear-quadratic control;

D O I：

10.1109/9.895575

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we analyze the set of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar N-player linear-quadratic differential game. We show that in general there exist at most 2(N) - 1 solutions of the (ARE) that give rise to a Nash equilibrium. In particular we analyze the number of equilibria as a function of the autonomous growth parameter and present both necessary and sufficient conditions for the existence of a unique solution of the ARE.

引用

页码：2363 / 2368

页数：6

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