Low-Rank Second-Order Splitting of Large-Scale Differential Riccati Equations

Research output: Contribution to journalArticle


We apply first- and second-order splitting schemes to the differential Riccati equation. Such equations are very important in e.g. linear quadratic regulator (LQR) problems, where they provide a link between the state of the system and the optimal input. The methods can also be extended to generalized Riccati equations, e.g. arising from LQR problems given in implicit form. In contrast to previously proposed schemes such as BDF or Rosenbrock methods, the splitting schemes exploit the fact that the nonlinear and affine parts of the problem, when considered in isolation, have closed-form solutions. We show that if the solution possesses low-rank structure, which is frequently the case, then this is preserved by the method. This feature is used to implement the methods efficiently for large-scale problems. The proposed methods are expected to be competitive, as they at most require the solution of a small number of linear equation systems per time step. Finally, we apply our low-rank implementations to the Riccati equations arising from two LQR problems. The results show that the rank of the solutions stay low, and the expected orders of convergence are observed.


  • Tony Stillfjord
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Differential Riccati equation, large-scale, low-rank, Riccati differential equation, splitting methods
Original languageEnglish
Pages (from-to)2791-2796
JournalIEEE Transactions on Automatic Control
Issue number10
Publication statusPublished - 2015
Publication categoryResearch

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)

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Related research output

Stillfjord, T., 2015, Centre for Mathematical Sciences, Lund University. 129 p.

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