# Chance Constrained Stochastic Optimal Control for Arbitrarily Disturbed LTI Systems Via the One-Sided Vysochanskij-Petunin Inequality

arXiv: https://arxiv.org/abs/2303.12295 · HTML: https://mlsanity.com/paper/2303.12295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [Multi-Modal Spatio-Temporal Graph Neural Network with Mixture of Experts for Soil Organic Carbon Prediction](https://mlsanity.com/paper/2606.16580/) (2026)

## Abstract (arXiv)

While many techniques have been developed for chance constrained stochastic optimal control with Gaussian disturbance processes, far less is known about computationally efficient methods to handle non-Gaussian processes. In this paper, we develop a method for solving chance constrained stochastic optimal control problems for linear time-invariant systems with general additive disturbances with finite moments and unimodal chance constraints. We propose an open-loop control scheme for multi-vehicle planning, with both target sets and collision avoidance constraints. Our method relies on the one-sided Vysochanskij-Petunin inequality, a tool from statistics used to bound tail probabilities of unimodal random variables. Using the one-sided Vysochanskij-Petunin inequality, we reformulate each chance constraint in terms of the expectation and standard deviation. While the reformulated bounds are conservative with respect to the original bounds, they have a simple and closed form, and are amenable to difference of convex optimization techniques. We demonstrate our approach on a multi-satellite rendezvous problem.