Adaptive high-order splitting schemes for large-scale differential Riccati equations
Stillfjord, Tony LU
(2017)
In Numerical Algorithms
78(4).
p.1129-1151
- Abstract
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical to employ structural properties of the matrix-valued solution, or the computational cost and storage requirements become infeasible. Our main contribution is therefore to formulate these high-order splitting schemes in an efficient way by utilizing a low-rank factorization. Previous results indicated that this was impossible for methods of order higher than 2, but our new approach overcomes these difficulties. In addition, we demonstrate that the proposed methods contain natural embedded error... (More)
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical to employ structural properties of the matrix-valued solution, or the computational cost and storage requirements become infeasible. Our main contribution is therefore to formulate these high-order splitting schemes in an efficient way by utilizing a low-rank factorization. Previous results indicated that this was impossible for methods of order higher than 2, but our new approach overcomes these difficulties. In addition, we demonstrate that the proposed methods contain natural embedded error estimates. These may be used, e.g., for time step adaptivity, and our numerical experiments in this direction show promising results.
(Less)
- author
- Stillfjord, Tony
LU
- publishing date
- 2017-09-23
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Adaptivity, Differential Riccati equations, High order, Large-scale, Splitting schemes
- in
- Numerical Algorithms
- volume
- 78
- issue
- 4
- pages
- 23 pages
- publisher
- Springer
- external identifiers
-
- scopus:85029766825
- ISSN
- 1017-1398
- DOI
- 10.1007/s11075-017-0416-8
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2017, The Author(s).
- id
- 37c8133b-b587-4c98-959d-aa3f9e36b96b
- date added to LUP
- 2024-01-23 17:32:17
- date last changed
- 2024-02-26 09:02:22
@article{37c8133b-b587-4c98-959d-aa3f9e36b96b,
abstract = {{<p>We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical to employ structural properties of the matrix-valued solution, or the computational cost and storage requirements become infeasible. Our main contribution is therefore to formulate these high-order splitting schemes in an efficient way by utilizing a low-rank factorization. Previous results indicated that this was impossible for methods of order higher than 2, but our new approach overcomes these difficulties. In addition, we demonstrate that the proposed methods contain natural embedded error estimates. These may be used, e.g., for time step adaptivity, and our numerical experiments in this direction show promising results.</p>}},
author = {{Stillfjord, Tony}},
issn = {{1017-1398}},
keywords = {{Adaptivity; Differential Riccati equations; High order; Large-scale; Splitting schemes}},
language = {{eng}},
month = {{09}},
number = {{4}},
pages = {{1129--1151}},
publisher = {{Springer}},
series = {{Numerical Algorithms}},
title = {{Adaptive high-order splitting schemes for large-scale differential Riccati equations}},
url = {{http://dx.doi.org/10.1007/s11075-017-0416-8}},
doi = {{10.1007/s11075-017-0416-8}},
volume = {{78}},
year = {{2017}},
}