2024/12/03 by Lea Bold, Friedrich Philipp, Bold, Lea +5 · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Numerical methods for differential equations #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2412.02811
openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work, we propose a novel kEDMD scheme to approximate nonlinear control systems accompanied by an in-depth error analysis. Key features are regularization-based robustness and an adroit decomposition into micro and macro grids enabling flexible sampling. But foremost, we prove proportionality, i.e., explicit dependence on the distance to the (controlled) equilibrium, of the derived bound on the full approximation error. Leveraging this key property, we rigorously show that asymptotic stability of the data-driven surrogate (control) system implies asymptotic stability of the original (control) system and vice versa.