CDC_2025 Workshop

Speaker: Igor Mezić (mezic@ucsb.edu), UC Santa Barbara, USA

Igor Mezić works on operator-theoretic methods in nonlinear dynamical systems and control theory and their applications in fluid dynamics, energy efficient design and operations and complex systems dynamics. He did his Dipl. Ing. in Mechanical Engineering in 1990 at the University of Rijeka, Croatia and his Ph. D. in Applied Mechanics at the California Institute of Technology. Dr. Mezić was a postdoctoral researcher at the Mathematics Institute, University of Warwick, UK in 1994-95. From 1995 to 1999 he was a member of Mechanical Engineering Department at the University of California, Santa Barbara where he is currently a Professor. In 2000-2001 he has worked as an Associate Professor at Harvard University in the Division of Engineering and Applied Sciences. He won the Alfred P. Sloan Fellowship, NSF CAREER Award from NSF and the George S. Axelby Outstanding Paper Award on ”Control of Mixing” from IEEE. He also won the United Technologies Senior Vice President award for Science and Technology Special Achievement Prize in 2007. He was an Editor of Physica D: Nonlinear Phenomena and an Associate Editor of the Journal of Applied Mechanics and SIAM Journal on Control and Optimization. Dr. Mezić is a Fellow of the American Physical Society (APS), Fellow of Society of Industrial and Applied Mathematics (SIAM), the Director of the Center for Energy E!cient Design and Head of Buildings and Design Solutions Group at the Institute for Energy Efficiency at the University of California, Santa Barbara.

Abstract: I will describe the approach to analysis, control and machine learning of dynamical systems based on Koopman Operator Theory (KOT). It produces predictive models amenable to (feedback) control applications. KOT has deep mathematical roots and I will discuss its basic tenets, starting from linear systems, continuing with lifting of nonlinear systems, enabling modeling, stability analysis and control. A number of examples will be discussed, including use in soft robotics, neural network training and online games. 

Speaker: Armin Lederer (armin.lederer@nus.edu.sg), ETH Zurich, Switzerland

Armin Lederer received the B.Sc., M.Sc., and Dr. Ing. degree in electrical and computer en- gineering from the Technical University of Munich, Germany, in 2015, 2018, and 2023, respectively. From 2023 to 2025, he was a postdoctoral researcher at the Learning and Adaptive Systems Group in the Department of Computer Science at ETH Zurich, Switzerland. Since 2025, he is an assistant professor in the department of electrical and computer engineering at the National University of Singapore. He was recipient of the Rohde & Schwarz PhD thesis award, a scholarship of the German National Scholarship Foundation, the Dimitris N. Chorafas Foundation Award in Computer Science, and finalist for the European Systems & Control PhD Thesis Award. His current research interests include the stability and safety of data-driven control systems, control with stochastic models, and probabilistic machine learning in closed-loop systems.

Abstract: Integrating structural prior information such as physics information into regression offers great promises to improve data efficiency of learning techniques, but formal results remain sparse. Starting from Gaussian process regression, we exemplarily illustrate how such structural knowledge can be expressed through linear operators, which subsequently can be included into supervised learning. We start with the example of Koopman operators, for which we derive dedicated kernels. This kernel enables learning in invariant subspaces of the Koopman operator by exploiting the direct connection between a kernel's hypothesis space and its feature map, immediately guaranteeing Koopman equivariance for GP models learned with this kernel. As a second example, we consider the Bellman operator, based on which we derive a kernel for learning value functions from temporal differences. The GP model resulting from this kernel enables the exploitation of upper confidence bounds in reinforcement learning, such that regret bounds can be proven. The benefits of our operator-informed priors in terms of sample complexity for learning are theoretically demonstrated and illustrated in numerical experiments.

Speakers: 

Max Beier, TU Munich, Germany
Max Beier obtained his Bachelor of Mechanical Engineering in 2020 at Baden-Wuerttemberg Cooperative State University Stuttgart with Bosch. His interest in learning from data where models from first principles fail drove him to enroll in the Robotics, Cognition, Intelligence Master at the Technical University of Munich, where he graduated in 2023. During his studies, he came to love systems and control as a framework for building models in the face of complex interactions. Since fall 2023, he has been pursuing his PhD with Prof. Hirche. He is particularly interested in learning practical dynamical systems representations in terms of utilizing the inherent structure in dynamical systems data, provable learning theoretic guarantees, and uncertainty quantification. 

Nicolas Hoischen, TU Munich, Germany
Nicolas Hoischen received the B.Sc. in Electronic and Electrical Engineering from the École Polytechnique Fédérale de Lausanne (EPFL) and the M.Sc. in Information Technology and Electrical Engineering from ETH Zurich in 2023. He is currently working towards the Ph.D. degree with the Chair of Information-Oriented Control, School of Computation, Information and Technology at the Technical University of Munich. His current research interests include data-driven and operator-theoretic methods for optimal control, as well as risk-aware decision-making in robotics and uncertain dynamical systems. 
 

Abstract: This talk presents a unified, nonparametric, data-driven framework for learning finite-dimensional representations of infinite-dimensional evolution operators in control systems, with applications to forecasting and optimal control. Drawing on tools from statistical learning and machine learning, we introduce a natural definition of the control Koopman operator that follows directly from discrete-time nonlinear dynamics. Unlike prior approaches that require operator families indexed by control values or operators acting on input sequences, our formulation involves only a single control Koopman operator, where evaluating inputs and feedback laws is formalized as linear operations on the observable space. Through the representer theorem for operators in reproducing kernel Hilbert spaces, finite data guarantees finite-rank estimators, and linear algebra enables computations to be finite-dimensional without loss of precision, even for infinite-dimensional observables. These ideas extend seamlessly to conditional expectation operators and infinitesimal generators, providing a unified treatment for both deterministic and stochastic control systems. Our learning algorithms are modular and expressive, achieving universal approximation for nonlinear systems while accommodating arbitrary state-control couplings. Moreover, they can handle large-scale control systems via sketching-based techniques and integrate seamlessly into optimal control and reinforcement learning pipelines.

Speaker: Jorge Cortès (jocortes@ucsd.edu), UC San Diego, USA

Jorge Cortès joined the Department of Mechanical and Aerospace Engineering at UCSD in 2007. He received the Licenciatura degree in mathematics from the Universidad de Zaragoza, Zaragoza, Spain, in 1997, and a Ph.D. in engineering mathematics from the Universidad Carlos III de Madrid, Madrid, Spain, in 2001. He was a Postdoctoral Research Associate at the Systems, Signals, and Control Department, University of Twente, Enschede, The Netherlands (from January to June 2002), and at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign (from August 2002 to September 2004). From 2004 to 2007, he was an assistant professor with the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz. He received a NSF CAREER award in 2006 and was the recipient of the 2006 Spanish Society of Applied Mathematics Young Researcher Prize. He is the author of the book Geometric, Control and Numerical Aspects of Nonholonomic Systems (New York: Springer-Verlag, 2002) and a co-author of the book Distributed Control of Robotic Networks (Princeton: Princeton University Press, 2009). He has co-authored papers that have won the 2008 IEEE Control Systems Outstanding Paper Award, the 2009 SIAM Review SIGEST selection from the SIAM Journal on Control and Optimization, and the 2012 O. Hugo Schuck Best Paper Award in the Theory category.He is a IEEE Fellow and a IEEE Control Systems Society Distinguished Lecturer. He has served in the Editorial Boards of the European Journal of Control, IEEE Transactions on Automatic Control, and Systems and Control Letters. He currently serves in the Editorial Board of IEEE Control Systems Magazine, SIAM Journal on Control and Optimization, and Journal of Geometric Mechanics.

Abstract: Koopman operator methods offer a physically-informed approach to unveil the underlying structure of dynamical systems from data and produce principled dynamic models describing the evolution of physical phenomena. The linearity of the operator, its spectral properties, and the tight connection with physical constraints and geometric structures provide a powerful tool for efficient computational learning and prediction of complex systems. Koopman-based approximations are also used for control as they provide low-complexity, finite-dimensional, physically-meaningful dynamical models from data.  For systems without inputs, the accuracy of these approximations can be analyzed in regards to the Koopman operator and critically relies on the quality of the dictionary of observables. For systems with inputs, accuracy is harder to characterize since the role of the input is fundamentally different from the role of the state: without a priori knowledge of the input signal, there is not enough information to predict the system's trajectories.  This talk describes the key role played by the notion of invariance in providing a comprehensive mathematical framework for Koopman operator-based modeling of control systems, formal measures to assess prediction accuracy and dictionary quality, as well as to develop efficient computational techniques to identify approximate Koopman-invariant subspaces and eigenfunctions with rigorous convergence and accuracy
guarantees.

Speaker: Karl Worthmann (karl.worthmann@tu-ilmenau.de), TU Ilmenau, Germany

Karl Worthmann received his Ph.D. degree in mathematics from the University of Bayreuth, Germany, in 2012. 2014 he became assistant professor for ”Differential Equations” at Technische Universität Ilmenau (TU Ilmenau), Germany. 2019 he was promoted to full professor after receiving the Heisenberg-professorship ”Optimization-based Control” by the German Research Foundation. He was recipient of the Ph.D. Award from the City of Bayreuth, Germany, and stipend of the German National Academic Foundation. 2013 he has been appointed Junior Fellow of the Society of Applied Mathematics and Mechanics (GAMM), where he served as speaker in 2014 and 2015. Karl Worthmann’s current research interests include systems and control theory with a particular focus on nonlinear model predictive control, stability analysis, and data-driven control.

Abstract: Extended dynamic mode decomposition, embedded in the Koopman framework [3], is a widely applied technique to predict the evolution of an observable along the flow of dynamical systems. However, despite its popularity, the error analysis is still fragmentary. We provide an analysis of the full approximation error [2] including an extension to control systems [1, 6]. To this end, we show Koopman invariance of suitably-constructed reproducing kernel Hilbert spaces (RKHS) and leverage approximation-theoretic arguments for (regularised) kernel EDMD. Then, we extend the results to control affine systems and demonstrate the applicability of the data-driven surrogate models for model predictive control [5, 4], see also the recent overview paper [7].

References:
[1] L. Bold, F. M. Philipp, M. Schaller, and K. Worthmann. Kernelbased Koopman approximants for control: Flexible sampling, error analysis, and stability, 2024. SIAM Journal on Control and Optimization, arxiv.org/abs/2412.02811.

[2] F. Köhne, F. M. Philipp, M. Schaller, A. Schiela, and K. Worthmann. L∞error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition. SIAM Journal on Applied Dynamical Systems, 24(1):501–529, 2025.

[3] I. Mezic. Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynamics, 41:309–325, 2005.

[4] I. Schimperna, L. Bold, J. Köhler, K. Worthmann, and L. Magni. Stability of data-driven koopman mpc with terminal conditions, 2025. https://arxiv.org/abs/2511.21248.

[5] I. Schimperna, K. Worthmann, M. Schaller, L. Bold, and L. Magni. Data-driven model predictive control: Asymptotic stability despite approximation errors exemplified in the Koopman framework, 2025. arXiv:2505.05951.

[6] P. Schmitz, L. Bold, F. M. Philipp, M. Rosenfelder, P. Eberhard, H. Ebel, and K. Worthmann. On excitation of control-affine systems and its use for data-driven Koopman approximants, 2025. arXiv:2511.03734.

[7] R. Strässer, K. Worthmann, I. Mezic, J. Berberich, M. Schaller, and F. Allgöwer. An overview of Koopman-based control: From error bounds to closed-loop guarantees. Annual Reviews in Control, 61:101035, 2026.

Speakers:

Frank Allgöwer (frank.allgower@ist.uni-stuttgart.de), University of Stuttgart, Germany

Frank Allgöwer is director of the Institute for Systems Theory and Automatic Control at the University of Stuttgart in Germany and professor in the mechanical engineering department there. His current research interests are to develop new methods for data-based control, optimization-based control and networked control. Frank has published over 500 papers and received several recognitions for his work including the IFAC Outstanding Service Award, the IEEE CSS Distinguished Member Award, the State Teaching Award of the German state of Baden-Württemberg, and the Leibniz Prize of the Deutsche Forschungsgemeinschaft. Frank has been the President of the International Federation of Automatic Control (IFAC) for the years 2017-2020. He was Editor for the journal Automatica from 2001 to 2015 and is editor for the Springer Lecture Notes in Control and Information Science book series. He was Vice-president for Technical Activities of the IEEE Control Systems Society for the years 2013/14 and was on the EUCA Council for 2001-2004. From 2012 until 2020, Frank also served as Vice-President of Germany's most important research funding agency, the German Research Foundation (DFG).

Julian Berberich (julian.berberich@ist.uni-stuttgart.de), University of Stuttgart, Germany

Julian Berberich is a Lecturer (Akademischer Rat) at the Institute for Systems Theory and Automatic Control at the University of Stuttgart, Germany. He received his Ph.D. in Mechanical Engineering in 2022, and a Master’s degree in Engineering Cybernetics in 2018, both from the University of Stuttgart, Germany. In 2022, he was a visiting researcher at ETH Zürich, Switzerland. He is a recipient of the 2022 George S. Axelby Outstanding Paper Award as well as the Outstanding Student Paper Award at the 59th IEEE Conference on Decision and Control in 2020. His research interests include data-driven analysis and control as well as quantum computing.

Robin Strässer (robin.straesser@ist.uni-stuttgart.de), University of Stuttgart, Germany

Robin Strässer is currently a PhD student at the Institute for Systems Theory and Automatic Control at the University of Stuttgart under the supervision of Prof. Frank Allgöwer. He received a master's degree in Simulation Technology from the University of Stuttgart, Germany, in 2020. During his M.Sc., he spent six months at UC Santa Barbara, where he also carried out the research for his master's thesis under the supervision of Prof. James Rawlings. Since 2020, he has been a research and teaching assistant at the Institute for Systems Theory and Automatic Control and a member of the Graduate School Simulation Technology at the University of Stuttgart. His research interests include data-driven system analysis and control, with a focus on nonlinear systems, in particular by using the Koopman operator to obtain (bi-)linear surrogate models with error certificates. Robin Strässer received the Best Poster Award at the International Conference on Data-Integrated Simulation Science (SimTech2023) and the Best Paper Award at the European Robotics Forum (ERF2025).

Abstract: This talk presents recent advances in data-driven controller design for nonlinear dynamical systems, with a focus on ensuring closed-loop stability via Koopman operator theory. The Koopman operator enables the reformulation of a nonlinear control-affine system as an infinite-dimensional bilinear system, which can be approximated using Extended Dynamic Mode Decomposition (EDMD) with finite data and a finite dictionary. By integrating robust control strategies, we develop purely data-driven state-feedback controllers that explicitly account for approximation errors. In particular, we discuss the Stability- and certificate-oriented EDMD (SafEDMD) framework alongside a kernel-based EDMD variant, both yielding finite-dimensional bilinear surrogate models. Based on these data-driven, error-affected representations, we provide rigorous closed-loop guarantees through proportional error bounds, thereby enabling reliable controller design for nonlinear systems. This approach leads to a nonlinear controller parameterization that can be efficiently computed using semidefinite programming. Numerical examples demonstrate the effectiveness of the proposed methods and highlight their advantages over existing Koopman-based control approaches.

Speaker: Elad Hazan (ehazan@princeton.edu), Princeton University, USA

Elad Hazan is a professor of computer science at Princeton University. His research focuses on the design and analysis of algorithms for basic problems in machine learning and optimization. Among his contributions are the co-invention of the AdaGrad algorithm for deep learning, the first sublinear-time algorithms for convex optimization, and online nonstochastic control theory. He is the recipient of the Bell Labs Prize, the IBM Goldberg best paper award twice, a European Research Council grant, a Marie Curie fellowship, Google Research Award and is an ACM fellow. He served on the steering committee of the Association for Computational Learning and was program chair for the Conference on Learning Theory 2015. He is the co-founder and director of Google AI Princeton.

Abstract: Learning in dynamical systems is a fundamental challenge underlying modern sequence modeling. This talk presents a provably efficient framework for learning in any bounded and Lipschitz nonlinear dynamical system, establishing sublinear regret guarantees in a dimension-free setting. Our approach combines Koopman lifting, Luenberger observers, and, crucially, spectral filtering to show that a broad class of nonlinear dynamics are learnable. These insights motivate a new neural architecture, the Spectral Transform Unit (STU), which we will describe and present preliminary experiments on open benchmarks of language modelling and dynamical systems.

Speaker: Massimiliano Pontil (Massimiliano.Pontil@iit.it), Istituto Italiano di Tecnologia, Italia

Massimiliano Pontil is Principal Investigator at the Italian Institute of Technology, where he leads the Computational Statistics and Machine Learning Unit, and co-director of the ELLIS Unit Genoa. He is also Professor at University College London and a member of the UCL Centre for Artificial Intelligence. His research spans kernel methods, hyperparameter optimization, multitask and transfer learning, sparsity regularization, and statistical learning theory. Recent efforts include novel methods for learning linear evolution operators of dynamical systems
(see: https://github.com/Machine-Learning-Dynamical-Systems/kooplearn).

Abstract: This talk presents a framework for learning linear evolution operators of dynamical systems that admit an invariant distribution, with a particular focus on discrete stochastic systems. We introduce estimators that learn the restriction of the transfer operator to a reproducing kernel Hilbert space H and discuss forecasting and spectral bounds, highlighting the notion of metric distortion between H and the ambient L^2 space relative to the invariant measure. The bounds indicate that regularization and rank reduction are key to mitigating metric distortion. We also comment on the extent to which they apply to deterministic systems. Moreover, the bounds depend on a representation error that vanishes when H is invariant or dense in L^2. This motivates a method to learn the representation, or dictionary of basis functions, which is reminiscent of deep CCA approaches for self-supervised learning. We discuss the statistical properties of this approach, its ability to address inference tasks, and its strong performance on high-dimensional dynamical systems.