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Ndiaye, M. (2022) The Riccati Equation, Differential Transform, Rational Solutions and Applications. Applied Mathematics, 13, 774-792.
https://doi.org/10.4236/am.2022.139049

has been cited by the following article:

• TITLE: Matrix Riccati Equations in Optimal Control

  AUTHORS: Malick Ndiaye

  KEYWORDS: Optimal Control, Matrix Riccati Equation, Change of Variable

  JOURNAL NAME: Applied Mathematics, Vol.15 No.3, March 29, 2024

  ABSTRACT: In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.