A Spectral Perspective on Stochastic Control Barrier Functions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917354716266496 |
|---|---|
| author | Jang, Inkyu Mballo, Chams E. Tomlin, Claire J. Kim, H. Jin |
| author_facet | Jang, Inkyu Mballo, Chams E. Tomlin, Claire J. Kim, H. Jin |
| contents | Stochastic control barrier functions (SCBFs) provide a safety-critical control framework for systems subject to stochastic disturbances by bounding the probability of remaining within a safe set. However, synthesizing a valid SCBF that explicitly reflects the true safety probability of the system, which is the most natural measure of safety, remains a challenge. This paper addresses this issue by adopting a spectral perspective, utilizing the linear operator that governs the evolution of the closed-loop system's safety probability. We find that the dominant eigenpair of this Koopman-like operator encodes fundamental safety information of the stochastic system. The dominant eigenfunction is a natural and valid SCBF, with values that explicitly quantify the relative long-term safety of the state, while the dominant eigenvalue indicates the global rate at which the safety probability decays. A practical synthesis algorithm is proposed, termed power-policy iteration, which jointly computes the dominant eigenpair and an optimized backup policy. The method is validated using simulation experiments on safety-critical dynamics models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19813 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Spectral Perspective on Stochastic Control Barrier Functions Jang, Inkyu Mballo, Chams E. Tomlin, Claire J. Kim, H. Jin Systems and Control Optimization and Control Stochastic control barrier functions (SCBFs) provide a safety-critical control framework for systems subject to stochastic disturbances by bounding the probability of remaining within a safe set. However, synthesizing a valid SCBF that explicitly reflects the true safety probability of the system, which is the most natural measure of safety, remains a challenge. This paper addresses this issue by adopting a spectral perspective, utilizing the linear operator that governs the evolution of the closed-loop system's safety probability. We find that the dominant eigenpair of this Koopman-like operator encodes fundamental safety information of the stochastic system. The dominant eigenfunction is a natural and valid SCBF, with values that explicitly quantify the relative long-term safety of the state, while the dominant eigenvalue indicates the global rate at which the safety probability decays. A practical synthesis algorithm is proposed, termed power-policy iteration, which jointly computes the dominant eigenpair and an optimized backup policy. The method is validated using simulation experiments on safety-critical dynamics models. |
| title | A Spectral Perspective on Stochastic Control Barrier Functions |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2603.19813 |