  Data-driven control algorithms use observations of system dynamics to
construct an implicit model for the purpose of control. However, in practice,
data-driven techniques often require excessive sample sizes, which may be
infeasible in real-world scenarios where only limited observations of the
system are available. Furthermore, purely data-driven methods often neglect
useful a priori knowledge, such as approximate models of the system dynamics.
We present a method to incorporate such prior knowledge into data-driven
control algorithms using kernel embeddings, a nonparametric machine learning
technique based in the theory of reproducing kernel Hilbert spaces. Our
proposed approach incorporates prior knowledge of the system dynamics as a bias
term in the kernel learning problem. We formulate the biased learning problem
as a least-squares problem with a regularization term that is informed by the
dynamics, that has an efficiently computable, closed-form solution. Through
numerical experiments, we empirically demonstrate the improved sample
efficiency and out-of-sample generalization of our approach over a purely
data-driven baseline. We demonstrate an application of our method to control
through a target tracking problem with nonholonomic dynamics, and on
spring-mass-damper and F-16 aircraft state prediction tasks.
