On the data-sparsity of the solution of Riccati equations with applications to feedback control

2024/08/29 by Stefano Massei, Luca Saluzzi, Massei, Stefano +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2408.16569

openalex publication_date 2024/08/29 · openalex created_date 2024/09/22 · openalex updated_date 2026/07/28

Abstract

Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution also exhibits numerical quasiseparability. This property enables us to develop two efficient Riccati solvers. The first solver is applicable to the general quasiseparable case, while the second is tailored to the particular case of banded coefficients. Numerical experiments confirm the effectiveness of the proposed algorithms on both synthetic examples and case studies from the control of partial differential equations and agent-based models.

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