# Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets

arXiv: https://arxiv.org/abs/1805.07145 · HTML: https://mlsanity.com/paper/1805.07145/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2018.

## Built on by (most cited first, 3 of 3)

- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [Stochastic Model Predictive Control Utilizing Bayesian Neural Networks](https://mlsanity.com/paper/2303.14519/) (2023)
- [Online Constraint Tightening in Stochastic Model Predictive Control: A Regression Approach](https://mlsanity.com/paper/2310.02942/) (2023)

## Abstract (arXiv)

In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in analogy to robust MPC using a constraint tightening based on the concept of probabilistic reachable sets, which is shown to provide closed-loop fulfillment of chance constraints under a unimodality assumption on the disturbance distribution. A control scheme reverting to a backup solution from a previous time step in case of infeasibility is proposed, for which an asymptotic average performance bound is derived. Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.