"On Control and Random Dynamical Systems

in Reproducing Kernel Hilbert Spaces"





Boumediene Hamzı

(Yıldız Technical University)


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. These results collectively argue that there is a  reasonable passage from linear dynamical systems theory to a  data-based nonlinear dynamical systems theory through reproducing  kernel Hilbert spaces. This is joint work with J. Bouvrie (MIT).



Date:  Tuesday, May  6, 2014

Time: 15:40

Place: Mathematics Seminar Room, SA-141


Tea and cookies will be served before the seminar.