# Safe Control for Nonlinear Systems with Stochastic Uncertainty via Risk Control Barrier Functions

arXiv: https://arxiv.org/abs/2203.15892 · HTML: https://mlsanity.com/paper/2203.15892/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2022.

## Built on by (most cited first, 5 of 5)

- [A Generalizable Physics-informed Learning Framework for Risk Probability Estimation](https://mlsanity.com/paper/2305.06432/) (2023)
- [Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocation](https://mlsanity.com/paper/2305.13467/) (2023)
- [Safe Control using Learned Safety Filters and Adaptive Conformal Inference](https://mlsanity.com/paper/2604.18482/) (2026)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [Response-Aware Risk-Constrained Control Barrier Function With Application to Vehicles](https://mlsanity.com/paper/2603.24598/) (2026)

## Abstract (arXiv)

Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for enforcing safety related set-theoretic properties, such as forward invariance and reachability, of nonlinear dynamical systems. In this paper, we extend this rich framework to nonlinear discrete-time systems subject to stochastic uncertainty and propose a framework for assuring risk-sensitive safety in terms of coherent risk measures. To this end, we introduce risk control barrier functions (RCBFs), which are compositions of barrier functions and dynamic, coherent risk measures. We show that the existence of such barrier functions implies invariance in a coherent risk sense. Furthermore, we formulate conditions based on finite-time RCBFs to guarantee finite-time reachability to a desired set in the coherent risk. Conditions for risk-sensitive safety and finite-time reachability of sets composed of Boolean compositions of multiple RCBF are also formulated. We show the efficacy of the proposed method through its application to a cart-pole system in a safety-critical scenario.