Wasserstein Tube MPC with Exact Uncertainty Propagation
Abstract
We study model predictive control (MPC) problems for stochastic LTI systems, where the noise distribution is unknown, compactly supported, and only observable through a limited number of i.i.d. noise samples. Building upon recent results in the literature, which show that distributional uncertainty can be efficiently captured within a Wasserstein ambiguity set, and that such ambiguity sets propagate exactly through the system dynamics, we start by formulating a novel Wasserstein Tube MPC (WT-MPC) problem, with distributionally robust CVaR constraints. We then show that the WT-MPC problem: (1) is a direct generalization of the (deterministic) Robust Tube MPC (RT-MPC) to the stochastic setting; (2) through a scalar parameter, it interpolates between the data-driven formulation based on sample average approximation and the RT-MPC formulation, allowing us to optimally trade between safety and performance; (3) admits a tractable convex reformulation; and (4) is recursively feasible. We conclude the paper with a numerical comparison of WT-MPC and RT-MPC.
Keywords
Cite
@article{arxiv.2304.12093,
title = {Wasserstein Tube MPC with Exact Uncertainty Propagation},
author = {Liviu Aolaritei and Marta Fochesato and John Lygeros and Florian Dörfler},
journal= {arXiv preprint arXiv:2304.12093},
year = {2023}
}