# Stochastic Model Predictive Control for Sub-Gaussian Noise

arXiv: https://arxiv.org/abs/2503.08795 · HTML: https://mlsanity.com/paper/2503.08795/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2025.

## Built on by (most cited first, 4 of 4)

- [Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics](https://mlsanity.com/paper/2505.07594/) (2025)
- [Safe and Near-Optimal Control with Online Dynamics Learning](https://mlsanity.com/paper/2509.16650/) (2025)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise](https://mlsanity.com/paper/2605.09757/) (2026)

## Abstract (arXiv)

We propose a stochastic Model Predictive Control (MPC) framework that ensures closed-loop chance constraint satisfaction for linear systems with general sub-Gaussian process and measurement noise. By considering sub-Gaussian noise, we can provide guarantees for a large class of distributions, including time-varying distributions. Specifically, we first provide a new characterization of sub-Gaussian random vectors using matrix variance proxy, which can more accurately represent the predicted state distribution. We then derive tail bounds under linear propagation for the new characterization, enabling tractable computation of probabilistic reachable sets of linear systems. Lastly, we utilize these probabilistic reachable sets to formulate a stochastic MPC scheme that provides closed-loop guarantees for general sub-Gaussian noise. We further demonstrate our approach in simulations, including a challenging task of surgical planning from image observations.