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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2025.12.008

Matrix Riccati Equations in Optimal Control: A Differential Transform Method Approach

Malick Ndiaye*, Alexander Beckford, Addison Hoermann, Ryan Jimenez

Marist University, Poughkeepsie, NY 12601, USA.

*Corresponding author:Malick Ndiaye

Published: December 31,2025

Abstract

In this article, we investigate an application of the matrix Riccati equation (MRE) arising in the linear-quadratic regulator (LQR), a fundamental class of optimal control problems. The characterization of the control in the LQR setting depends critically on the integrability of the MRE. Unfortunately, there is no general way of solving the MRE. An analytic solution or closed-form solution to the MRE depends on how the coefficients of the equation are connected to each other. To address this limitation, we derive semi-analytic series solutions to the MRE by leveraging the power of the differential transform method (DTM). This approach yields an explicit series representation of both the Riccati solution and the corresponding optimal control. We further investigate the convergence properties of the proposed approximation by analyzing the logarithm of the squared approximation error (log-squared error), thereby providing quantitative insight into the accuracy and stability of the series solution.

Keywords

Matrix Riccati Equation; Linear Quadratic Regulator; Differential Transform Method

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How to cite this paper

Matrix Riccati Equations in Optimal Control: A Differential Transform Method Approach

How to cite this paper: Malick Ndiaye, Alexander Beckford, Addison Hoermann, Ryan Jimenez. (2025) Matrix Riccati Equations in Optimal Control: A Differential Transform Method Approach. Journal of Applied Mathematics and Computation9(4), 278-288.

DOI: http://dx.doi.org/10.26855/jamc.2025.12.008