  We consider the problem of optimal trajectory tracking for unknown systems. A
novel data-enabled predictive control (DeePC) algorithm is presented that
computes optimal and safe control policies using real-time feedback driving the
unknown system along a desired trajectory while satisfying system constraints.
Using a finite number of data samples from the unknown system, our proposed
algorithm uses a behavioural systems theory approach to learn a non-parametric
system model used to predict future trajectories. The DeePC algorithm is shown
to be equivalent to the classical and widely adopted Model Predictive Control
(MPC) algorithm in the case of deterministic linear time-invariant systems. In
the case of nonlinear stochastic systems, we propose regularizations to the
DeePC algorithm. Simulations are provided to illustrate performance and compare
the algorithm with other methods.
