Abstract

We consider the problem of optimal and constrained control 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 is grounded on insights from subspace identification and behavioral systems theory. In particular, we use raw unprocessed data assembled in a Hankel (or Page) matrix to predict and optimize over the future system behavior. In case of deterministic linear time-invariant systems, the DeePC algorithm is equivalent to standard Model Predictive Control (MPC). To cope with stochasticity and nonlinearity, we propose regularizations to the objective and constraints of the DeePC algorithm, e.g., promoting averaging and sparse selection of Hankel matrix columns. By using techniques from distributionally robust stochastic optimization and measure concentration results, we prove that these regularizations indeed robustify DeePC against corrupted data. Finally, we show through case studies that the robustified DeePC generally outperforms subsequent system identification and certainty-equivalence MPC, and we conclude by speculating upon possible reasons. All of our results are illustrated with experiments and simulations from aerial robotics, power electronics, and power systems.