Galerkin trial spaces and Davison-Maki methods for the numerical solution of differential Riccati equations

Maximilian Behr, Peter Benner and Jan Heiland

Applied Mathematics and Computation, 2021, vol. 410, issue C

Abstract: The differential Riccati equation appears in different fields of applied mathematics like control and system theory. Recently, Galerkin methods based on Krylov subspaces were developed for the autonomous differential Riccati equation. These methods overcome the prohibitively large storage requirements and computational costs of the numerical solution. Known solution formulas are reviewed and extended. Because of memory-efficient approximations, invariant subspaces for a possibly low-dimensional solution representation are identified. A Galerkin projection onto a trial space related to a low-rank approximation of the solution of the algebraic Riccati equation is proposed. The modified Davison-Maki method is used for time discretization. Known stability issues of the Davison-Maki method are discussed. Numerical experiments for large-scale autonomous differential Riccati equations and a comparison with high-order splitting schemes are presented.

Keywords: DIfferential Riccati equation; Davison-Maki method; Low-rank methods; Optimal control; Linear-quadratic regulator (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321004902
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321004902

DOI: 10.1016/j.amc.2021.126401

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().