Control Meets Learning Seminar
We consider the problem of optimal and constrained data-driven control for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our algorithm is grounded on insights from subspace identification and behavioral systems theory. In particular, we use raw unprocessed data assembled in a matrix time series for data-driven estimation and prediction. In case of deterministic linear time-invariant (LTI) systems, the DeePC algorithm is equivalent to standard Model Predictive Control (MPC). To cope with stochasticity and nonlinearity, we robustify the objective and constraints of DeePC by means of distributionally robust stochastic optimization resulting in regularized problem formulations. Finally, we relate our direct data-driven control approach to the indirect approach consisting of sequential system identification and certainty-equivalence control. We conclude that the direct approach can be derived as convex relaxation of the indirect approach, where the regularizations account for an implicit identification step. Our comparisons suggest that the direct approach is superior for control of nonlinear systems, whereas the indirect approach excels for stochastic LTI systems. All of our results are illustrated with experiments and simulations from aerial robotics, power electronics, and power systems.