Distributionally Robust Model Predictive Control with Total Variation Distance

TL;DR

This paper introduces a distributionally robust model predictive control framework using total variation distance, reformulating the problem for improved probabilistic guarantees and computational efficiency in linear systems.

Contribution

It presents a novel CVaR-based reformulation of distributionally robust MPC with total variation ambiguity sets, simplifying chance constraints for linear systems.

Findings

Enhanced probabilistic guarantees demonstrated through experiments

Reduced computational complexity for MPC with distributional robustness

Effective over-approximation of chance constraints

Abstract

This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk reformulation of the MPC optimization problem that is distributionally robust in the expected cost and chance constraints. The distributionally robust chance constraint is over-approximated as a simpler, tightened chance constraint that reduces the computational burden. Numerical experiments support our results on probabilistic guarantees and computational efficiency.