Title: On Control and Random Dynamical Systems in Reproducing Kernel Hilbert Spaces
Speaker: Dr. Boumediene Hamzi
Affiliation: Department of Mathematics of Imperial College
Location: CPSE seminar room (C615 Roderic Hill)
Time: 2:00pm

Abstract. We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems – with a reasonable expectation of success – once the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. In particular, we develop computable, non-parametric estimators approximating controllability and observability energy functions for nonlinear systems, and study the ellipsoids they induce. It is then shown that the controllability energy estimator provides a key means for approximating the invariant measure of an ergodic, stochastically forced nonlinear system. We also apply this approach to the problem of model reduction of nonlinear control systems. In all cases the relevant quantities are estimated from simulated or observed data. This is joint work with J. Bouvrie (Duke University).

About the speaker. Boumediene Hamzi is a Marie Curie Fellow at the Department of Mathematics of Imperial College. He obtained his Ph.D. in Control Theory from the University of Paris-Sud and then held different visiting academic positions at UCDavis, the MSRI and then Duke University. His current research interests are the analysis of control and random dynamical systems in Reproducing Kernel Hilbert Spaces in view of developing data-based methods for the analysis and prediction of random dynamical systems and control strategies for nonlinear systems on the basis of observed data (rather than a pre-described model).