Koopman-based controller design for nonlinear systems with closed-loop guarantees

Robin Strässer

ISBN 978-3-8325-6088-1
187 Seiten, Erscheinungsjahr: 2026
Preis: 40.00 €

This thesis closes this gap by presenting a systematic control framework for nonlinear systems that connects Koopman theory and data-driven modeling to robust control design with rigorous closed-loop guarantees. The framework consists of two main components. First, bilinear surrogate models are derived from data using Koopman operator theory, providing explicit residual error bounds that account for finite-data and approximation effects. Second, these surrogate models form the basis for designing robust state-feedback controllers that explicitly incorporate the model uncertainties, ensuring desired closed-loop properties of the underlying nonlinear system.

The framework in this thesis provides a rigorous and systematic foundation for Koopman-based control, establishing both numerical effectiveness and theoretical closed-loop guarantees, such as exponential stability and quadratic performance, via linear matrix inequalities and sum-of-squares relaxations.