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

Journal article
Authors Tony Stillfjord
Published in Numerical Algorithms
Volume 78
Issue 4
Pages 1129-1151
ISSN 1017-1398
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1129-1151
Language en
Links https://doi.org/10.1007/s11075-017-...
Keywords Adaptivity, Differential Riccati equations, High order, Large-scale, Splitting schemes
Subject categories Computational Mathematics, Control Engineering, Signal Processing

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 estimates. These may be used, e.g., for time step adaptivity, and our numerical experiments in this direction show promising results.

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