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arXiv · 2409.15448

Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach

Erfan Shakhesi·W. P. M. H. Heemels·Alexander Katriniok
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Abstract

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.

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Erfan Shakhesi, W. P. M. H. Heemels, Alexander Katriniok. 2024-09-23. Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach. https://doi.org/10.1109/cdc56724.2024.10886703

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