Year: 2025
Type: preprint
Abstract: The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework for data-fitting of control-affine mappings to increase the robustness margin in the associated system identification problem and, thus, to provide reliable bilinear EDMD schemes. In particular, guidelines for input selection based on subspace angles are deduced such that a desired threshold with respect to the minimal singular value is ensured. Moreover, we derive necessary and sufficient conditions of optimality for maximizing the minimal singular value. Further, we demonstrate the usefulness of the proposed approach using bilinear EDMD with control for nonholonomic robots.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Optimierungsbasierte und datengetriebene Steuerung und Regelung unter Nutzung portHamiltonscher Strukturen, G4794403668, G5086116315, Untersuchung der Mehrkörperdynamik und Regelung für den kollaborativen Transport elastischer Objekte mithilfe eines heterogenen Schwarms von fliegenden und fahrenden mobilen Robotern
OpenAlex ID: W4416021889
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