Numerical Method for a Class of Algebraic Riccati Equations

TL;DR

This paper introduces an iterative numerical method and an effective algorithm for solving coupled algebraic Riccati equations in two-player Nash differential games, supported by numerical examples across various matrix dimensions.

Contribution

It presents a novel iterative approach and an algorithm specifically designed for positive definite solutions of coupled algebraic Riccati equations in game theory.

Findings

Successful application to matrix Riccati equations of different sizes

Demonstrated convergence of the proposed iterative method

Validated effectiveness through numerical examples

Abstract

We study an iteration approach to solve the coupled algebraic Riccati equations when they appear in general two player closed-loop type Nash differential games over an infinite time horizon. Also, we propose an effective algorithm for finding positive definite solutions. In particular, we present various numerical examples connected with matrix Riccati equations according to different dimensions.