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Topic

Invariance as the key enabler for accurate Koopman-based approximations of dynamical systems

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鈥檚 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.

About the speaker

Jorge Cortes is a Professor and Cymer Corporation Endowed Chair in High Performance Dynamic Systems Modeling and Control in the Department of Mechanical and Aerospace Engineering, University of California, San Diego. He is the author of Geometric, Control and Numerical Aspects of Nonholonomic Systems (New York: Springer-Verlag, 2002) and co-author of Distributed Control of Robotic Networks (Princeton: Princeton University Press, 2009).  

He is a Fellow of IEEE, SIAM, and IFAC.  He has co-authored papers that have won the 2008 and the 2021 IEEE Control Systems Outstanding Paper Award, the 2009 SIAM Review SIGEST selection from the SIAM Journal on Control and Optimization, the 2012 O. Hugo Schuck Best Paper Award in the Theory category, the 2019 and 2023 IEEE Transactions on Control of Network Systems Outstanding Paper Award, and the 2025 IEEE Control Systems Letters Outstanding Paper Award.  At the IEEE Control Systems Society, he has been a Distinguished Lecturer (2010-2014), an elected member (2018-2020) of the Board of Governors, and Director of Operations (2019-2022) of its Executive Committee.  

His research interests include distributed control and optimization, network science and complex systems, learning for control, distributed decision making and autonomy, network neuroscience, and multi-agent coordination in robotic, power, and transportation networks.

Your host

Michelle Chong  Assistent professor at the Department of Mechanical Engineering.

is required but free of charge.