# Online Constraint Tightening in Stochastic Model Predictive Control: A Regression Approach

arXiv: https://arxiv.org/abs/2310.02942 · HTML: https://mlsanity.com/paper/2310.02942/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 8 of 8)

- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Stochastic data-driven model predictive control using Gaussian processes](https://mlsanity.com/paper/1908.01786/) (2019)
- [Constraint-Tightening and Stability in Stochastic Model Predictive Control](https://mlsanity.com/paper/1511.03488/) (2015)
- [Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets](https://mlsanity.com/paper/1805.07145/) (2018)
- [Recursively Feasible Stochastic Model Predictive Control using Indirect Feedback](https://mlsanity.com/paper/1812.06860/) (2018)
- [Stability and performance of stochastic predictive control](https://mlsanity.com/paper/1304.2581/) (2013)
- [Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints](https://mlsanity.com/paper/2110.04570/) (2021)

## Abstract (arXiv)

Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for tackling chance-constrained stochastic optimal control problems consists of reformulating the chance constraints as hard constraints with a constraint-tightening parameter. However, in such approaches, the choice of constraint-tightening parameter remains challenging, and guarantees can mostly be obtained assuming that the process noise distribution is known a priori. Moreover, the chance constraints are often not tightly satisfied, leading to unnecessarily high costs. This work proposes a data-driven approach for learning the constraint-tightening parameters online during control. To this end, we reformulate the choice of constraint-tightening parameter for the closed-loop as a binary regression problem. We then leverage a highly expressive glsgp model for binary regression to approximate the smallest constraint-tightening parameters that satisfy the chance constraints. By tuning the algorithm parameters appropriately, we show that the resulting constraint-tightening parameters satisfy the chance constraints up to an arbitrarily small margin with high probability. Our approach yields constraint-tightening parameters that tightly satisfy the chance constraints in numerical experiments, resulting in a lower average cost than three other state-of-the-art approaches.