A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation

被引：1

作者：

Banadaki, Mojtaba Dehghan ^{[1
]}

Navidi, Hamidreza ^{[1
]}

机构：

[1] Shahed Univ, Dept Appl Math, Tehran, Iran

来源：

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 2022年 / 10卷 / 04期

关键词：

Differential games; Feedback Nash equilibrium; Bellman's optimality principle; Bernoulli Tau method; DISTRIBUTED-ORDER; OPEN-LOOP; APPROXIMATION; EQUILIBRIUM;

D O I：

10.22034/cmde.2022.44213.1870

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present study, an efficient combination of the Tau method with the Bernoulli polynomials is proposed for computing the Feedback Nash equilibrium in differential games over a finite horizon. By this approach, the system of Hamilton-Jacobi-Bellman equations of a differential game derived from Bellman's optimality principle is transferred to a nonlinear system of algebraic equations solvable by using Newton's iteration method. Some illustrative examples are provided to show the accuracy and efficiency of the proposed numerical method.

引用

页码：894 / 904

页数：11

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