Regret and Conservatism of Distributionally Robust Constrained Stochastic Model Predictive Control

TL;DR

This paper investigates the conservatism and regret in distributionally robust stochastic model predictive control using moment-based ambiguity sets, providing insights into performance trade-offs when true uncertainty distributions are unknown.

Contribution

It introduces a novel analysis of accumulated sub-optimality and compares deterministic constraint tightening with the optimal approach under distributional uncertainty.

Findings

Quantifies conservatism of DR SMPC compared to known distribution case.

Provides bounds on regret due to distributional ambiguity.

Highlights the impact of distributional knowledge on control performance.

Abstract

We analyse the conservatism and regret of distributionally robust (DR) stochastic model predictive control (SMPC) when using moment-based ambiguity sets for modeling unknown uncertainties. To quantify the conservatism, we compare the deterministic constraint tightening while taking a DR approach against the optimal tightening when the exact distributions of the stochastic uncertainties are known. Furthermore, we quantify the regret by comparing the performance when the distributions of the stochastic uncertainties are known and unknown. Analysing the accumulated sub-optimality of SMPC due to the lack of knowledge about the true distributions of the uncertainties marks the novel contribution of this work.