Regularized and Distributionally Robust Data-Enabled Predictive Control

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.

Biography

Florian Dörfler is an Associate Professor at the Automatic Control Laboratory at ETH Zürich. He received his Ph.D. degree in Mechanical Engineering from the University of California at Santa Barbara in 2013, and a Diplom degree in Engineering Cybernetics from the University of Stuttgart in 2008. From 2013 to 2014 he was an Assistant Professor at the University of California Los Angeles. His primary research interests are centered around control, optimization, and system theory with applications in network systems such as electric power grids, robotic coordination, and social networks. He is a recipient of the distinguished young research awards by IFAC (Manfred Thoma Medal 2020) and EUCA (European Control Award 2020). His students were winners or finalists for Best Student Paper awards at the European Control Conference (2013, 2019), the American Control Conference (2016), the PES General Meeting (2020), and the PES PowerTech Conference (2017). He is furthermore a recipient of the 2010 ACC Student Best Paper Award, the 2011 O. Hugo Schuck Best Paper Award, the 2012-2014 Automatica Best Paper Award, the 2016 IEEE Circuits and Systems Guillemin-Cauer Best Paper Award, and the 2015 UCSB ME Best PhD award.