Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions
Year: 2025
Type: article
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.
Source: IEEE Control Systems Letters
Institution: Eindhoven University of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4411232059