Distributionally Robust Chance Constrained Data-enabled Predictive Control

TL;DR

This paper introduces a distributionally robust data-enabled predictive control algorithm for unknown stochastic linear systems, ensuring constraint satisfaction and strong out-of-sample performance using a novel data representation and optimization approach.

Contribution

It proposes a new DeePC method that leverages non-parametric data representation and distributionally robust optimization for constrained control of unknown stochastic systems.

Findings

Strong probabilistic guarantees for constraint satisfaction.

Effective out-of-sample performance demonstrated in case study.

End-to-end control design for unknown stochastic systems.

Abstract

We study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant 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 (i) a non-parametric representation of the subspace spanning the system behaviour, where past trajectories are sorted in Page or Hankel matrices; and (ii) 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 linear time-invariant systems. We illustrate the closed-loop performance of the DeePC in an aerial robotics case study.