Artificial Parameter Based Approximate Solutions of Non-Symmetric Matrix Riccati Differential Equation

Turetsky, Vladimir; Glizer, Valery Y.

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https://hdl.handle.net/2142/130249 Copy

Description

Title

Artificial Parameter Based Approximate Solutions of Non-Symmetric Matrix Riccati Differential Equation

Author(s)

• Turetsky, Vladimir
• Glizer, Valery Y.

Issue Date

2025-09-17

Keyword(s)

• Matrix Riccati differential equation
• Artificial parameter
• Series expansion

Abstract

Two alternative methods of approximate solution of a non-symmetric matrix Riccati differential equation are proposed. Both methods are based on the artificial parameter approach. In both cases, the equation is parametrized in such a way that the resulting equation coincides with the original one for the parameter equal to one. The solution of the parametrized equation is represented as a power series over the parameter. The conditions of strong uniform convergence of the series are derived, including the case where the parameter is equal to one. This yields sufficient conditions for the existence of a bounded solution in the entire time interval. Moreover, subject to these conditions, a partial series sum constitutes an approximate solution of the original equation. A numerical example dealing with a Nash linear-quadratic differential game is presented.

Publisher

Allerton Conference on Communication, Control, and Computing

Series/Report Name or Number

2025 61st Allerton Conference on Communication, Control, and Computing Proceedings

ISSN

2836-4503

Type of Resource

Text

Genre of Resource

Conference Paper/Presentation

Language

eng

Handle URL

https://hdl.handle.net/2142/130249&&

Copyright and License Information

Copyright 2025 is held by Vladimir Turetsky and Valery Y. Glizer.

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