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arXiv · 2606.17744

On the Solution of Large-scale Non-autonomous Differential Riccati Equations: a Numerical Study

Eugenio Mancinelli·Davide Palitta·Jens Saak
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Abstract

We explore the numerical solution of large-scale non-autonomous Differential Riccati Equations (DREs). While we assume to discretize the differential operator using a Backward Differentiation Formula (BDF) of order s, we solve the generalized Algebraic Riccati Equation (gARE) resulting at each time step by different state-of-the-art methods. In particular, we compare the performance of the inexact Newton- Kleinman method with line search and the low-rank RADI iteration, considering for both methods two different initialization strategies: zero initialization and warm-start. A comprehensive panel of numerical results illustrate the potential and limitations of these methods when employed within a numerical pipeline for the solution of DREs, rather than for the isolated solution of a single gARE, as commonly considered in the existing literature.

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Eugenio Mancinelli, Davide Palitta, Jens Saak. 2026-06-16. On the Solution of Large-scale Non-autonomous Differential Riccati Equations: a Numerical Study. https://arxiv.org/abs/2606.17744

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