SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems
This addresses the challenge of ensuring stability in data-driven control of nonlinear systems, which is incremental as it builds on existing EDMD methods with added guarantees.
The authors tackled the problem of designing controllers for nonlinear dynamical systems by proposing SafEDMD, a Koopman-based data-driven framework that provides closed-loop stability guarantees through semi-definite programming. The result is a method that offers proportional error bounds tailored to control tasks, demonstrated to outperform state-of-the-art methods in benchmark examples.
The Koopman operator serves as the theoretical backbone for machine learning of dynamical control systems, where the operator is heuristically approximated by extended dynamic mode decomposition (EDMD). In this paper, we propose SafEDMD, a novel stability- and feedback-oriented EDMD-based controller design framework. Our approach leverages a reliable surrogate model generated in a data-driven fashion in order to provide closed-loop guarantees. In particular, we establish a controller design based on semi-definite programming with guaranteed stabilization of the underlying nonlinear system. As central ingredient, we derive proportional error bounds that vanish at the origin and are tailored to control tasks. We illustrate the developed method by means of several benchmark examples and highlight the advantages over state-of-the-art methods.