Using the Koopman operator, nonlinear systems can be
expressed as infinite-dimensional linear systems. Data-driven methods
can then be used to approximate a finite-dimensional Koopman operator,
which is particularly useful for system identification, control, and
state estimation tasks. However, approximating large Koopman operators
is numerically challenging, leading to unstable Koopman operators
being identified for otherwise stable systems.
This talk will present a selection of techniques to regularize the Koopman regression
problem, including a novel H-infinity norm regularizer. In particular,
how to re-pose the system identification problem in order to leverage
numerically efficient optimization tools, such as linear matrix
inequalities, will be presented. This talk is based on the pre-print
arxiv