# Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Risk

arXiv: https://arxiv.org/abs/1802.07903 · HTML: https://mlsanity.com/paper/1802.07903/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2018.

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

- [Risk-Conditioned Distributional Soft Actor-Critic for Risk-Sensitive Navigation](https://mlsanity.com/paper/2104.03111/) (2021)
- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [Game-Theoretic Planning for Autonomous Driving among Risk-Aware Human Drivers](https://mlsanity.com/paper/2205.00562/) (2022)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [A Generalizable Physics-informed Learning Framework for Risk Probability Estimation](https://mlsanity.com/paper/2305.06432/) (2023)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [Uncertainty Principles in Risk-Aware Statistical Estimation](https://mlsanity.com/paper/2104.14283/) (2021)
- [Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systems](https://mlsanity.com/paper/2505.09734/) (2025)

## Abstract (arXiv)

In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set distance to formulate a safety risk-constrained optimal control problem. Our reformulation method using an extremal representation of the safety risk measure provides a computationally tractable dynamic programming solution. A useful byproduct of the proposed solution is the notion of a risk-constrained safe set, which is a new stochastic safety verification tool. We also establish useful connections between the risk-constrained safe sets and the popular probabilistic safe sets. The tradeoff between the risk tolerance and the mean performance of our controller is examined through an inventory control problem.