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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1129-1151
Number of pages23
JournalNumerical Algorithms
Volume78
Issue number4
DOIs
Publication statusPublished - 2017 Sept 23
Externally publishedYes

Subject classification (UKÄ)

  • Computational Mathematics

Free keywords

  • Adaptivity
  • Differential Riccati equations
  • High order
  • Large-scale
  • Splitting schemes

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