Robin Strässer

Nicolas Chatzikiriakos, Robin Strässer, Frank Allgöwer et al.

In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly unbounded support and leverage tools from statistical learning theory to derive finite sample identification error bounds. To this end, we solve the bilinear identification problem by solving a set of linear and affine identification problems, by a particular choice of a control input during the data collection phase. We provide a priori as well as data-dependent finite sample identification error bounds on the individual matrices as well as ellipsoidal bounds, both of which are structurally suitable for control. Further, we integrate the structure of the derived identification error bounds in a robust controller design to obtain an exponentially stable closed-loop. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds. Moreover, we note appealing connections of our results to indirect data-driven control of general nonlinear systems through Koopman operator theory and discuss how our results may be applied in this setup.

Robin Strässer, Julian Berberich, Manuel Schaller et al.

Data-driven control of nonlinear systems from input-output measurements remains a fundamental challenge, as existing approaches with rigorous closed-loop guarantees predominantly require access to full state measurements. In this paper, we address this gap by proposing a data-driven output-feedback controller design method for nonlinear systems that provides provable closed-loop guarantees while operating solely on measured input-output data. Our approach combines Koopman operator theory with an extended state representation of the nonlinear system constructed from input-output trajectories. This allows us to obtain a bilinear surrogate model directly from data, on which robust state-feedback design methods can be applied. By exploiting the observability of the underlying nonlinear system, we establish exponential stability of the extended state, which in turn implies exponential convergence of the original system state to the origin. Finally, we validate our theoretical findings in numerical simulations.

Robin Strässer, Manuel Schaller, Karl Worthmann et al.

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.