Adaptive high-order splitting schemes for large-scale differential Riccati equations
Artikel i vetenskaplig tidskrift, 2018

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.

Large-scale

Differential Riccati equations

High order

Adaptivity

Splitting schemes

Författare

Tony Stillfjord

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Numerical Algorithms

1017-1398 (ISSN)

Vol. 78 4 1129-1151

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Signalbehandling

DOI

10.1007/s11075-017-0416-8

Mer information

Senast uppdaterat

2018-08-15