ABSTRACT
How can we predict the trajectory of a free-falling object in a gravitational field? The classical model-based approach does it by solving a differential equation. Obtaining the differential equation, however, requires knowledge of physics and some hand derivations. In addition, the equation involves physical parameters that should be known a priori or measured. An alternative approach using generic machine learning methods requires instead observed data, hyper-parameter tuning, and substantial computations. This talk presents another data-driven approach that does not require precise knowledge of physics, hand derivations, or physical parameters, but still exploits the prior knowledge that the data is generated by a linear constant-coefficient differential equation. Unlike the machine learning methods, the method presented involves no hyper-parameter tuning, uses only five trajectories as data, and amounts to solving a system of linear equations. The approach is moreover applicable to analysis and control of general linear time-invariant systems, some classes of nonlinear systems, and linear parameter-varying systems.
SPEAKER
Ivan Markovsky received his Ph.D. degree in Electrical Engineering from the Katholieke Universiteit Leuven in February 2005. From 2006 to 2012 he was an Assistant Professor at the School of Electronics and Computer Science of the University of Southampton, from 2012 to 2022 an Associate Professor at the Vrije Universiteit Brussel, and since 2023 an ICREA professor at CIMNE. He is a recipient of an ERC starting grant “Structured low-rank approximation: Theory, algorithms, and applications” 2010–2015 and Householder Prize honorable mention 2008. His main research interests are computational methods for system theory, identification, and data-driven control in the behavioral setting.