Convergence analysis for the exponential Lie splitting scheme applied to the abstract differential Riccati equation
(2015) In Preprint without journal information- Abstract
- We consider differential Riccati equations (DREs).
These equations arise in many areas and are very important within the field of optimal control. In particular, DREs provide the crucial link between the state and the optimal input in the solution of linear quadratic regulator (LQR) problems.
For the approximation of the solutions to DREs we consider the recently introduced splitting methods, with the aim of proving convergence orders in the space of Hilbert--Schmidt operators. The use of this abstract setting yields stronger than usual temporal convergence results, and also implies that these are independent of a subsequent (reasonable) spatial discretization.
The main result is that the exponential Lie... (More) - We consider differential Riccati equations (DREs).
These equations arise in many areas and are very important within the field of optimal control. In particular, DREs provide the crucial link between the state and the optimal input in the solution of linear quadratic regulator (LQR) problems.
For the approximation of the solutions to DREs we consider the recently introduced splitting methods, with the aim of proving convergence orders in the space of Hilbert--Schmidt operators. The use of this abstract setting yields stronger than usual temporal convergence results, and also implies that these are independent of a subsequent (reasonable) spatial discretization.
The main result is that the exponential Lie splitting is first-order convergent, under no artificial regularity assumptions. As side-effects of the analysis, we also acquire concise proofs of the existence and positivity of the exact solutions to abstract DREs, in a more general setting than previously considered. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5265742
- author
- Stillfjord, Tony
LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- unpublished
- subject
- keywords
- Differential Riccati equation, splitting, error analysis, convergence order, Hilbert-Schmidt operators
- in
- Preprint without journal information
- pages
- 12 pages
- publisher
- Manne Siegbahn Institute
- ISSN
- 0348-7911
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- ac225587-b3ee-4d68-8172-b92a8a33d2a8 (old id 5265742)
- date added to LUP
- 2016-04-04 13:50:21
- date last changed
- 2018-11-21 21:16:39
@article{ac225587-b3ee-4d68-8172-b92a8a33d2a8, abstract = {{We consider differential Riccati equations (DREs).<br/><br> These equations arise in many areas and are very important within the field of optimal control. In particular, DREs provide the crucial link between the state and the optimal input in the solution of linear quadratic regulator (LQR) problems. <br/><br> For the approximation of the solutions to DREs we consider the recently introduced splitting methods, with the aim of proving convergence orders in the space of Hilbert--Schmidt operators. The use of this abstract setting yields stronger than usual temporal convergence results, and also implies that these are independent of a subsequent (reasonable) spatial discretization.<br/><br> The main result is that the exponential Lie splitting is first-order convergent, under no artificial regularity assumptions. As side-effects of the analysis, we also acquire concise proofs of the existence and positivity of the exact solutions to abstract DREs, in a more general setting than previously considered.}}, author = {{Stillfjord, Tony}}, issn = {{0348-7911}}, keywords = {{Differential Riccati equation; splitting; error analysis; convergence order; Hilbert-Schmidt operators}}, language = {{eng}}, publisher = {{Manne Siegbahn Institute}}, series = {{Preprint without journal information}}, title = {{Convergence analysis for the exponential Lie splitting scheme applied to the abstract differential Riccati equation}}, url = {{https://lup.lub.lu.se/search/files/6217252/5275368.pdf}}, year = {{2015}}, }