Data Driven Learning and Control seminar series is organized by the Information and Decision Science Lab at Cornell University and aims to explore the latest advancements and interdisciplinary approaches to data-driven learning and control systems.
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Invariance as the key enabler for accurate Koopman-based approximations of dynamical systems
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.
Bio: Jorge Cortés is a professor and holder of the Cymer Corporation Endowed Chair in High Performance Dynamic Systems Modeling and Control at the Department of Mechanical and Aerospace Engineering at the University of California, San Diego. He received the Licenciatura degree in mathematics from the Universidad de Zaragoza, Spain, in 1997, and the Ph.D. degree in engineering mathematics from the Universidad Carlos III de Madrid, Spain, in 2001. He held postdoctoral positions at the Systems, Signals and Control Department of the University of Twente in 2002 and at the Coordinated Science Laboratory of the University of Illinois at Urbana-Champaign from 2002 to 2004. He was an Assistant Professor with the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz from 2004 to 2007.
Cortés’ research interests are in systems and control, cooperative control, network optimization, distributed decision making and autonomy, systems orchestration, network science and complex systems, game theory, multi-agent coordination in robotics, transportation, power systems, and neuroscience, nonsmooth analysis, and geometric mechanics. His research is characterized by its interdisciplinary character and the connections between solid theoretical foundations, development of computational methods, and applications. His research program seeks to unveil the science and engineering that explains and enhances the operation of network systems. The ultimate aim is to understand the mechanisms that make complex networks function the way they do, and to use this knowledge to develop systematic methods to design better networks.