Distributionally Robust Chance Constrained Data-enabled Predictive\n Control

Abstract

We study the problem of finite-time constrained optimal control of unknown\nstochastic linear time-invariant systems, which is the key ingredient of a\npredictive control algorithm -- albeit typically having access to a model. We\npropose a novel distributionally robust data-enabled predictive control (DeePC)\nalgorithm which uses noise-corrupted input/output data to predict future\ntrajectories and compute optimal control inputs while satisfying output chance\nconstraints. The algorithm is based on (i) a non-parametric representation of\nthe subspace spanning the system behaviour, where past trajectories are sorted\nin Page or Hankel matrices; and (ii) a distributionally robust optimization\nformulation which gives rise to strong probabilistic performance guarantees. We\nshow that for certain objective functions, DeePC exhibits strong out-of-sample\nperformance, and at the same time respects constraints with high probability.\nThe algorithm provides an end-to-end approach to control design for unknown\nstochastic linear time-invariant systems. We illustrate the closed-loop\nperformance of the DeePC in an aerial robotics case study.\n