# Safe Control Design through Risk-Tunable Control Barrier Functions

arXiv: https://arxiv.org/abs/2309.10251 · HTML: https://mlsanity.com/paper/2309.10251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2023.

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

- [SafePG: Safe and Globally Optimal Reinforcement Learning with Hard Constraints](https://mlsanity.com/paper/2609.14076/) (2026)

## Abstract (arXiv)

We consider the problem of designing controllers to guarantee safety in a class of nonlinear systems under uncertainties in the system dynamics and/or the environment. We define a class of uncertain control barrier functions (CBFs), and formulate the safe control design problem as a chance-constrained optimization problem with uncertain CBF constraints. We leverage the scenario approach for chance constrained optimization to develop a risk-tunable control design that provably guarantees the satisfaction of CBF safety constraints up to a user-defined probabilistic risk bound, and provides a trade-off between the sample complexity and risk tolerance. We demonstrate the performance of this approach through simulations on a quadcopter navigation problem with obstacle avoidance constraints.