Data-driven distributionally robust MPC for systems with uncertain dynamics
Abstract
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected data and an approximate model of the dynamics to formulate a finite-horizon optimization problem. To account for both the uncertainty related to the dynamics and the disturbance acting on the system, we resort to a distributionally robust formulation that optimizes the cost expectation while satisfying Conditional Value-at-Risk constraints with respect to the worst-case probability distributions of the uncertainties within an ambiguity set defined using the Wasserstein metric. Using results from the distributionally robust optimization literature we derive a tractable finite-dimensional convex optimization problem with finite-sample guarantees for the class of convex piecewise affine cost and constraint functions. The performance of the proposed algorithm is demonstrated in closed-loop simulation on a simple numerical example.
Keywords
Cite
@article{arxiv.2209.08869,
title = {Data-driven distributionally robust MPC for systems with uncertain dynamics},
author = {Francesco Micheli and Tyler Summers and John Lygeros},
journal= {arXiv preprint arXiv:2209.08869},
year = {2022}
}