A Tunable Universal Formula for Safety-Critical Control
CoRR(2024)
摘要
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 - 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.
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