# Receding-horizon Stochastic Model Predictive Control with Hard Input Constraints and Joint State Chance Constraints

arXiv: https://arxiv.org/abs/1506.08471 · HTML: https://mlsanity.com/paper/1506.08471/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2015.

## Built on by (most cited first, 8 of 8)

- [Safe Chance Constrained Reinforcement Learning for Batch Process Control](https://mlsanity.com/paper/2104.11706/) (2021)
- [PC-Gym: Benchmark Environments For Process Control Problems](https://mlsanity.com/paper/2410.22093/) (2024)
- [A learning-based approach to stochastic optimal control under reach-avoid constraint](https://mlsanity.com/paper/2412.16561/) (2024)
- [Least Squares and Marginal Log-Likelihood Model Predictive Control using Normalizing Flows](https://mlsanity.com/paper/2409.17632/) (2024)
- [A Stochastic Online Forecast-and-Optimize Framework for Real-Time Energy Dispatch in Virtual Power Plants under Uncertainty](https://mlsanity.com/paper/2309.08642/) (2023)
- [Convex Chance-Constrained Stochastic Control under Uncertain Specifications with Application to Learning-Based Hybrid Powertrain Control](https://mlsanity.com/paper/2601.18313/) (2026)
- [Iterative Model-Learning Scheme via Gaussian Processes for Nonlinear Model Predictive Control of (Semi-)Batch Processes](https://mlsanity.com/paper/2604.22672/) (2026)
- [Joint Chance Constrained Safe-Optimal Control](https://mlsanity.com/paper/2606.30829/) (2026)

## Abstract (arXiv)

This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states. A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during prediction by parametrizing the control law as an affine function of the disturbances. Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization. The joint state chance constraints are conservatively approximated as a collection of individual chance constraints that are subsequently relaxed via the Cantelli-Chebyshev inequality. Feasibility of the SOCP is guaranteed by softening the approximated chance constraints using the exact penalty function method. Closed-loop stability in a stochastic sense is established by establishing that the states satisfy a geometric drift condition outside of a compact set such that their variance is bounded at all times. The SMPC approach is demonstrated using a continuous acetone-butanol-ethanol fermentation process, which is used for production of high-value-added drop-in biofuels.