Distributionally Robust Chance Constrained Data-Enabled Predictive Control

In this article we study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant (LTI) systems, which is the key ingredient of a predictive control algorithm—albeit typically having access to a model. We propose a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints. The algorithm is based on 1) a nonparametric representation of the subspace spanning the system behavior, where past trajectories are sorted in Page or Hankel matrices; and 2) a distributionally robust optimization formulation which gives rise to strong probabilistic performance guarantees. We show that for certain objective functions, DeePC exhibits strong out-of-sample performance, and at the same time respects constraints with high probability. The algorithm provides an end-to-end approach to control design for unknown stochastic LTI systems. We illustrate the closed-loop performance of the DeePC in an aerial robotics case study.