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arXiv · 2506.13011

Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions

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

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.

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Erfan Shakhesi, Alexander Katriniok, W. P. M. H. Heemels. 2025-06-16. Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions. https://doi.org/10.1109/lcsys.2025.3578971

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