  Data-enabled predictive control (DeePC) for linear systems utilizes data
matrices of recorded trajectories to directly predict new system trajectories,
which is very appealing for real-life applications. In this paper we leverage
the universal approximation properties of neural networks (NNs) to develop
neural DeePC algorithms for nonlinear systems. Firstly, we point out that the
outputs of the last hidden layer of a deep NN implicitly construct a basis in a
so-called neural (feature) space, while the output linear layer performs affine
interpolation in the neural space. As such, we can train off-line a deep NN
using large data sets of trajectories to learn the neural basis and compute
on-line a suitable affine interpolation using DeePC. Secondly, methods for
guaranteeing consistency of neural DeePC and for reducing computational
complexity are developed. Several neural DeePC formulations are illustrated on
a nonlinear pendulum example.
