Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918060057690112 |
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| author | Shakhesi, Erfan Katriniok, Alexander Heemels, W. P. M. H. |
| author_facet | Shakhesi, Erfan Katriniok, Alexander Heemels, W. P. M. H. |
| contents | Learning-based methods have gained popularity for training candidate Control Barrier Functions (CBFs) to satisfy the CBF conditions on a finite set of sampled states. However, since the CBF is unknown a priori, it is unclear which sampled states belong to its zero-superlevel set and must satisfy the CBF conditions, and which ones lie outside it. Existing approaches define a set in which all sampled states are required to satisfy the CBF conditions, thus introducing conservatism. In this paper, we address this issue for robust discrete-time CBFs (R-DTCBFs). Furthermore, we propose a class of R-DTCBFs that can be used in an online optimization problem to synthesize safe controllers for general discrete-time systems with input constraints and bounded disturbances. To train such an R-DTCBF that is valid not only on sampled states but also across the entire region, we employ a verification algorithm iteratively in a counterexample-guided approach. We apply the proposed method to numerical case studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions Shakhesi, Erfan Katriniok, Alexander Heemels, W. P. M. H. Optimization and Control Systems and Control Learning-based methods have gained popularity for training candidate Control Barrier Functions (CBFs) to satisfy the CBF conditions on a finite set of sampled states. However, since the CBF is unknown a priori, it is unclear which sampled states belong to its zero-superlevel set and must satisfy the CBF conditions, and which ones lie outside it. Existing approaches define a set in which all sampled states are required to satisfy the CBF conditions, thus introducing conservatism. In this paper, we address this issue for robust discrete-time CBFs (R-DTCBFs). Furthermore, we propose a class of R-DTCBFs that can be used in an online optimization problem to synthesize safe controllers for general discrete-time systems with input constraints and bounded disturbances. To train such an R-DTCBF that is valid not only on sampled states but also across the entire region, we employ a verification algorithm iteratively in a counterexample-guided approach. We apply the proposed method to numerical case studies. |
| title | Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2506.13011 |