  We introduce a general framework for robust data-enabled predictive control
(DeePC) for linear time-invariant (LTI) systems. The proposed framework enables
us to obtain model-free optimal control for LTI systems based on noisy
input/output data. More specifically, robust DeePC solves a min-max
optimization problem to compute the optimal control sequence that is resilient
to all possible realizations of the uncertainties in the input/output data
within a prescribed uncertainty set. We present computationally tractable
reformulations of the min-max problem with various uncertainty sets.
Furthermore, we show that even though an accurate prediction of the future
behavior is unattainable in practice due to inaccessibility of the perfect
input/output data, the obtained robust optimal control sequence provides
performance guarantees for the actually realized input/output cost. We further
show that the robust DeePC generalizes and robustifies the regularized DeePC
(with quadratic regularization or 1-norm regularization) proposed in the
literature. Finally, we demonstrate the performance of the proposed robust
DeePC algorithm on high-fidelity, nonlinear, and noisy simulations of a
grid-connected power converter system.
