Distributionally Robust Chance Constrained Data-enabled Predictive Control

Jeremy Coulson; John Lygeros; Florian Dörfler

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arXiv · 2006.01702

Distributionally Robust Chance Constrained Data-enabled Predictive Control

Jeremy Coulson·John Lygeros·Florian Dörfler

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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.

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Jeremy Coulson, John Lygeros, Florian Dörfler. 2020-06-02. Distributionally Robust Chance Constrained Data-enabled Predictive Control. https://arxiv.org/abs/2006.01702

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