Adaptive high-order splitting schemes for large-scale differential Riccati equations
Journal article, 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

Author

Tony Stillfjord

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Numerical Algorithms

1017-1398 (ISSN)

Vol. 78 4 1129-1151

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.1007/s11075-017-0416-8

More information

Latest update

8/15/2018