# Adaptive Stochastic MPC under Unknown Noise Distribution

arXiv: https://arxiv.org/abs/2204.01107 · HTML: https://mlsanity.com/paper/2204.01107/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 3 Apr 2022.

## Builds on (most cited first, 4 of 4)

- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Constraint-Tightening and Stability in Stochastic Model Predictive Control](https://mlsanity.com/paper/1511.03488/) (2015)
- [Stochastic MPC with Offline Uncertainty Sampling](https://mlsanity.com/paper/1606.06056/) (2016)
- [An Improved Constraint-Tightening Approach for Stochastic MPC](https://mlsanity.com/paper/1409.8183/) (2014)

## Abstract (arXiv)

In this paper, we address the stochastic MPC (SMPC) problem for linear systems, subject to chance state constraints and hard input constraints, under unknown noise distribution. First, we reformulate the chance state constraints as deterministic constraints depending only on explicit noise statistics. Based on these reformulated constraints, we design a distributionally robust and robustly stable benchmark SMPC algorithm for the ideal setting of known noise statistics. Then, we employ this benchmark controller to derive a novel robustly stable adaptive SMPC scheme that learns the necessary noise statistics online, while guaranteeing time-uniform satisfaction of the unknown reformulated state constraints with high probability. The latter is achieved through the use of confidence intervals which rely on the empirical noise statistics and are valid uniformly over time. Moreover, control performance is improved over time as more noise samples are gathered and better estimates of the noise statistics are obtained, given the online adaptation of the estimated reformulated constraints. Additionally, in tracking problems with multiple successive targets our approach leads to an online-enlarged domain of attraction compared to robust tube-based MPC. A numerical simulation of a DC-DC converter is used to demonstrate the effectiveness of the developed methodology.