# Inverse Optimal Safety Filters

arXiv: https://arxiv.org/abs/2112.08225 · HTML: https://mlsanity.com/paper/2112.08225/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2021.

## Built on by (most cited first, 3 of 3)

- [Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions](https://mlsanity.com/paper/2309.04492/) (2023)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Unifying Controller Design for Stabilizing Nonlinear Systems with Norm-Bounded Control Inputs](https://mlsanity.com/paper/2403.03030/) (2024)

## Abstract (arXiv)

CBF-QP safety filters are pointwise minimizers of the control effort at a given state vector, i.e., myopically optimal at each time instant. But are they optimal over the entire infinite time horizon? What does it even mean for a controlled dynamic systems to be "optimally safe" as opposed to, conventionally "optimally stable"? When disturbances, deterministic and stochastic, have unknown upper bounds, how should safety be defined to allow a graceful degradation under disturbances? Can safety filters be designed to guarantee such weaker safety properties as well as the optimality of safety over the infinite time horizon? We pose and answer these questions for general systems affine in control and disturbances and illustrate the answers using several examples. In the process, using the existing QP safety filters, as well as more general safety-ensuring feedbacks, we generate entire families of safety filters which are optimal over the infinite horizon though they are conservative (favoring safety over `alertness') relative to the standard QP.