2020/12/02 by Charles Poussot-Vassal, Poussot-Vassal, Charles, Pauline Kergus +3
Engineering · Mathematics · Physics and Astronomy · #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical methods for differential equations #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2012.01040
openalex publication_date 2020/12/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim, following an academic driving example described by a linear partial differential equation, it is shown how the Loewner-based interpolation may be an essential ingredient for control design and stability analysis. More specifically, the interpolatory framework is first used to approximate the irrational model by a rational one that can be used for model-based control, and secondly, it is used for direct data-driven control design, showing equivalent results. Finally, this interpolation framework is employed for estimating the stability of the interconnection of the irrational model with a rational controller.