Equivalence Between Contraction and Koopman Approaches and Its Application in Nonlinear System Identification

Explore the connections between the Koopman operator framework and contraction analysis for nonlinear systems in this 54-minute GERAD Research Center seminar. Delve into the equivalence of these approaches for stability analysis and control design problems, based on a novel relation with the Kazantzis-Kravaris-Luenberger observer. Examine the extension of these findings to discrete-time systems and learn about a new data-driven method for learning stable models of nonlinear systems. Discover how this approach uses Koopman embeddings to lift the original state space to a higher-dimensional linear manifold, allowing for unconstrained optimization while enforcing model stability through direct parameterization of stable linear systems.