Data-Driven Approaches to Stochastic Linear Systems? Willems' Fundamental Lemma Through the Eyes of Wiener (Prof. Timm Faulwasser, Institute for Energy Systems, TU Dortmund)
Systems & Control Seminar
Abstract
In this seminar, motivated by ongoing developments for multi-energy systems, we discuss recent progress of data-driven descriptions for stochastic LTI systems. Leveraging polynomial chaos expansions (PCE) of random variables, the origins of which date back to Norbert Wiener [1], we answer the question of how to tailor the fundamental lemma of Willems et al. [2] to stochastic systems. We illustrate how the knowledge or the estimation of past noise realizations allows the construction of Hankel matrices which in turn enable propagation of non-Gaussian and Gaussian uncertainties with non-parametric system descriptions [3,4]. We discuss how this can be used for output-feedback MPC of stochastic LTI systems [5-7] and for uncertainty propagation without explicit model knowledge [3,4]. Finally, we comment on behavioral implications of our approach [4,8].
[1] Wiener, Norbert. "The homogeneous chaos." American Journal of Mathematics 60, no. 4 (1938): 897-936.
[2] Willems, Jan C., Paolo Rapisarda, Ivan Markovsky, and Bart LM De Moor. "A note on persistency of excitation." Systems & Control Letters 54, no. 4 (2005): 325-329.
[3] Pan, Guanru, Ruchuan Ou, and Timm Faulwasser. "On a stochastic fundamental lemma and its use for data-driven optimal control." IEEE Transactions on Automatic Control (2022).
[4] Faulwasser, Timm, Ruchuan Ou, Guanru Pan, Philipp Schmitz, and Karl Worthmann. "Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again." Annual Reviews in Control 55 (2023): 92-117.
[5] Coulson, Jeremy, John Lygeros, and Florian Dörfler. "Data-enabled predictive control: In the shallows of the DeePC." In 2019 18th European Control Conference (ECC), pp. 307-312. IEEE, 2019.
[6] Berberich, Julian, Johannes Köhler, Matthias A. Müller, and Frank Allgöwer. "Data-driven model predictive control with stability and robustness guarantees." IEEE Transactions on Automatic Control 66, no. 4 (2020): 1702-1717.
[7] Pan, Guanru, Ruchuan Ou, and Timm Faulwasser. "On Data-Driven Stochastic Output-Feedback Predictive Control." arXiv preprint arXiv:2211.17074 (2022).
[8] Markovsky, Ivan, and Florian Dörfler. "Behavioral systems theory in data-driven analysis, signal processing, and control." Annual Reviews in Control 52 (2021): 42-64.
Biographical information
Timm Faulwasser has studied engineering cybernetics at the University of Stuttgart. From 2008 until 2012 he was a member of the International Max Planck Research School for Analysis, Design and Optimization in Chemical and Biochemical Process Engineering Magdeburg; he obtained his Ph.D. from the Department of Electrical Engineering and Information Technology, Otto-von-Guericke University Magdeburg, Germany in 2012. After postdocs at École Polytechnique Fédérale de Lausanne (EPFL), Switzerland and at Karlsruhe Institute for Technology, Germany, he joined the Department of Electrical Engineering and Information Technology at TU Dortmund University, Germany in 2019. Currently, he serves as associate editor for IEEE Transactions on Automatic Control, IEEE Control System Letters, and Mathematics of Control Systems and Signals. His research interests are optimization and control of uncertain nonlinear systems and cyber-physical networks with applications in energy, mechatronics, process control, and beyond.
Date
27. Jun. 202316:00 - 17:00
