A Tunable Universal Formula for Safety-Critical Control
<|reference_start|>A Tunable Universal Formula for Safety-Critical Control: Sontag's universal formula is a widely-used technique for stabilizing control through control Lyapunov functions, and it has been extended to address safety-critical control in recent years by incorporating control barrier functions (CBFs). However, how to derive a universal formula that satisfies requirements on essential properties, including safety, robustness, and smoothness, is still an open problem. To address this challenge, this paper introduces a novel solution - a tunable universal formula - by incorporating a (state-dependent) tunable scaling term into Sontag's universal formula. This tunable scaling term enables the regulation of safety control performances, allowing the attainment of desired properties through a proper selection. Furthermore, we extend this tunable universal formula to address safety-critical control problems with norm-bounded input constraints, showcasing its applicability across diverse control scenarios. Finally, we demonstrate the efficacy of our method through a collision avoidance example, investigating the essential properties including safety, robustness, and smoothness under various tunable scaling terms.<|reference_end|>
@article{li2024a,
    title={A Tunable Universal Formula for Safety-Critical Control},
    author={Ming Li, Zhiyong Sun, Patrick J. W. Koelewijn, and Siep Weiland},
    journal={arXiv preprint arXiv:2403.06285},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06285},
    primaryClass={eess.SY cs.SY math.OC}
}