Generalized Koopman operators for data-driven predictive control

Abstract

Data-driven predictive control raises the question whether learned models can support the same closed-loop guarantees as physics-based model predictive control.

This talk addresses the question via the generalized Koopman (GeKo) operator, a single closed-form operator on a product Hilbert space whose Petrov–Galerkin truncations converge to it. Linear and bilinear Koopman models are recovered as special cases. Finite-dimensional GeKo models come with a certificate that bounds the residual with respect to the true dynamics. The operator also yields a nonlinear fundamental lemma, which connects the approach to behavioural data-driven predictive control.

The talk then show how GeKo models are learned from data via multi-step Khatri–Rao kernel regression, which reduces the multi-step prediction error relevant for predictive control. The talk concludes by discussing how the certified residual bounds can serve as a bounded model mismatch for input-to-state stability and robust MPC designs.

Short Bio

Mircea Lazar is a Full Professor on Constrained Control of Complex Systems in the Department of Electrical Engineering at Eindhoven University of Technology (TU/e), The Netherlands. He received the Dipl.Ing. and MSc degrees in Control Engineering from the “Gh. Asachi” Technical University of Iasi, Romania, and the PhD degree in control systems from TU/e in 2006, for which he received the EECI PhD Award in 2007. He was a visiting professor at Boston University, the University of Stuttgart and Université Grenoble Alpes.

His research focuses on model predictive control, Koopman operator theory for data-driven control, stability of nonlinear and hybrid systems, and optimization methods for control, with applications ranging from high-tech systems to power networks. He chaired the IEEE CSS Technical Committee on Hybrid Systems (2011-2016), is Chair of IFAC TC 2.3 on Non-Linear Control Systems, and served as Associate Editor for IEEE Transactions on Automatic Control. He has supervised 15 PhD students and published more than 70 journal papers.