# Optimal Covariance Control for Stochastic Systems Under Chance Constraints

arXiv: https://arxiv.org/abs/1804.02829 · HTML: https://mlsanity.com/paper/1804.02829/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2018.

## Built on by (most cited first, 7 of 7)

- [Maximum entropy optimal density control of discrete-time linear systems and Schr"odinger bridges](https://mlsanity.com/paper/2204.05263/) (2022)
- [Real-time Cooperative Vehicle Coordination at Unsignalized Road Intersections](https://mlsanity.com/paper/2205.01278/) (2022)
- [Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems](https://mlsanity.com/paper/2504.09836/) (2025)
- [Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions](https://mlsanity.com/paper/2605.04246/) (2026)
- [Mode Reduction for Markov Jump Systems](https://mlsanity.com/paper/2205.02697/) (2022)
- [Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems](https://mlsanity.com/paper/2603.07092/) (2026)
- [Mutual Information Optimal Density Control of Linear Systems and Generalized Schr"odinger Bridges with Reference Refinement](https://mlsanity.com/paper/2605.09349/) (2026)

## Abstract (arXiv)

This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian distribution to another Gaussian distribution while minimizing a cost function. To the best of our knowledge, covariance steering problems have never been discussed with probabilistic chance constraints although it is a natural extension. In this work, first we show that, unlike the case with no chance constraints, the covariance steering with chance constraints problem cannot decouple the mean and covariance steering sub-problems. Then we propose an approach to solve the covariance steering with chance constraints problem by converting it to a semidefinite programming problem. The proposed algorithm is verified using two simple numerical simulations.