🤖 AI Summary
This work addresses the problem of designing data-driven controllers for nonlinear dynamical systems with verifiable closed-loop stability guarantees. Methodologically, it introduces a Koopman operator-based control framework that embeds stability certificates directly into the Extended Dynamic Mode Decomposition (EDMD) modeling process—specifically, by enforcing a vanishing proportional error bound at the origin and jointly optimizing the controller and a Lyapunov function via semidefinite programming (SDP), grounded in Lyapunov stability theory. The key contributions are: (i) a stability-oriented EDMD paradigm that enables control-objective-driven, quantifiable characterization of model approximation error; and (ii) an end-to-end stability certification mechanism. Experimental evaluation on multiple benchmark nonlinear systems demonstrates that the proposed approach achieves strict closed-loop stability while significantly improving control accuracy and robustness compared to existing methods.
📝 Abstract
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 certificate-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.