"On Control and Random Dynamical Systems
in Reproducing Kernel Hilbert Spaces"
By
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.