  We develop an online data-enabled predictive (ODeePC) control method for
optimal control of unknown systems, building on the recently proposed DeePC
[1]. Our proposed ODeePC method leverages a primal-dual algorithm with
real-time measurement feedback to iteratively compute the corresponding
real-time optimal control policy as system conditions change. The proposed
ODeePC conceptual-wise resembles standard adaptive system identification and
model predictive control (MPC), but it provides a new alternative for the
standard methods. ODeePC is enabled by computationally efficient methods that
exploit the special structure of the Hankel matrices in the context of DeePC
with Fast Fourier Transform (FFT) and primal-dual algorithm. We provide
theoretical guarantees regarding the asymptotic behavior of ODeePC, and we
demonstrate its performance through numerical examples.
