Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914051586523136 |
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| author | Shakhesi, Erfan Heemels, W. P. M. H. Katriniok, Alexander |
| author_facet | Shakhesi, Erfan Heemels, W. P. M. H. Katriniok, Alexander |
| contents | Discrete-time Control Barrier Functions (DTCBFs) form a powerful control theoretic tool to guarantee safety and synthesize safe controllers for discrete-time dynamical systems. In this paper, we provide an optimization-based algorithm, inspired by the $α$BB algorithm, for the verification of a candidate DTCBF, i.e., either verifying a given candidate function as a valid DTCBF or falsifying it by providing a counterexample for a general nonlinear discrete-time system with input constraints. This method is applicable whether a corresponding control policy is known or unknown. We apply our method to a numerical case study to illustrate its efficacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach Shakhesi, Erfan Heemels, W. P. M. H. Katriniok, Alexander Optimization and Control Systems and Control Discrete-time Control Barrier Functions (DTCBFs) form a powerful control theoretic tool to guarantee safety and synthesize safe controllers for discrete-time dynamical systems. In this paper, we provide an optimization-based algorithm, inspired by the $α$BB algorithm, for the verification of a candidate DTCBF, i.e., either verifying a given candidate function as a valid DTCBF or falsifying it by providing a counterexample for a general nonlinear discrete-time system with input constraints. This method is applicable whether a corresponding control policy is known or unknown. We apply our method to a numerical case study to illustrate its efficacy. |
| title | Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2409.15448 |