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Analysis of institutional authors

Hernandez, VAuthorIbanez, JjAuthorPeinado, JCorresponding Author

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October 29, 2024
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A GMRES-based BDF method for solving differential Riccati equations

Publicated to:Applied Mathematics And Computation. 196 (2): 613-626 - 2008-03-01 196(2), DOI: Doi 10.1016/J.Amc.2007.06.021

Authors: Hernandez, Vicente; Ibanez, Jacinto Javier; Peinado, Jesus; Arias, Enrique

Affiliations

Univ Castilla La Mancha, Dept Sis Informat - Author
Univ Politecn Valencia, Dept Sist Informat & Comp - Author

Abstract

Differential Riccati equations play a fundamental role in control theory, for example, optimal control, filtering and estimation, decoupling and order reduction, etc. The most popular codes to solve stiff differential Riccati equations use backward differentiation formula (BDF) methods. In this paper, a new approach to solve differential Riccati equations by means of a BDF method is described. In each step of these methods an algebraic Riccati equation is obtained, which is solved by means of Newton's method. In the standard approach, this system is transformed into a Sylvester equation, which could be solved by means of the well-known Bartels-Stewart method. In our code, we obtain a system of linear equations, defined from a Kronecker product of matrices related to coefficient matrices of the differential Riccati equation, that is solved by means of the iterative generalized minimum residual (GMRES) method. We have also implemented an efficient matrix-vector product in order to reduce the computational and storage cost of the GMRES method. The above approach has been applied in the development of an algorithm to solve differential Riccati equations. The accuracy and efficiency of this algorithm has been compared with the BDF algorithm that uses the Bartels-Stewart method. Experimental results show the advantages of the new algorithm. (C) 2007 Elsevier Inc. All rights reserved.

Keywords

ÁlgebraAlgebraic riccati equationBdf methodsComputational methodsControl theoryDifferential riccati equationsGmres methodsMatrixNumerical-integrationOptimal control systemsProblem solvingRiccati equations

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Applied Mathematics And Computation due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2008, it was in position 61/175, thus managing to position itself as a Q2 (Segundo Cuartil), in the category Mathematics, Applied. Notably, the journal is positioned en el Cuartil Q2 para la agencia Scopus (SJR) en la categoría Computational Mathematics.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-09-03:

  • WoS: 7
  • Scopus: 8

Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Hernández Ambato, Valeria Katherine) .

the author responsible for correspondence tasks has been Peinado Pinilla, Jesús.