  We introduce a novel data-driven order reduction method for nonlinear control
systems, drawing on recent progress in machine learning and statistical
dimensionality reduction. The method rests on the assumption that the nonlinear
system behaves linearly when lifted into a high (or infinite) dimensional
feature space where balanced truncation may be carried out implicitly. This
leads to a nonlinear reduction map which can be combined with a representation
of the system belonging to a reproducing kernel Hilbert space to give a closed,
reduced order dynamical system which captures the essential input-output
characteristics of the original model. Empirical simulations illustrating the
approach are also provided.
