Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach
<|reference_start|>Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach: 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 $\alpha$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.<|reference_end|>
@article{shakhesi2024optimization-based,
    title={Optimization-based Verification of Discrete-time Control Barrier
  Functions: A Branch-and-Bound Approach},
    author={Erfan Shakhesi, W.P.M.H. Heemels, Alexander Katriniok},
    journal={arXiv preprint arXiv:2409.15448},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.15448},
    primaryClass={math.OC cs.SY eess.SY}
}