A Tunable Universal Formula for Safety-Critical Control
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912404399456256 |
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| author | Li, Ming Sun, Zhiyong Koelewijn, Patrick J. W. Weiland, Siep |
| author_facet | Li, Ming Sun, Zhiyong Koelewijn, Patrick J. W. Weiland, Siep |
| contents | Sontag's universal formula is a widely used technique for stabilizing control through control Lyapunov functions. Recently, it has been extended to address safety-critical control by incorporating control barrier functions (CBFs). However, deriving a universal formula that satisfies requirements on essential properties, including safety, smoothness, and robustness against input disturbances, 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 term into Sontag's formula. This tunable term enables the regulation of safety-critical control performances, allowing the attainment of desired properties through a proper selection of tunable terms. Generally, the tunable universal formula can be seen as a controller that improves the quadratic program (QP)-synthesized controllers in terms of robustness and smoothness, while also reducing the conservatism (corresponding to robustness) in Sontag's formula. Furthermore, we extend the 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 two-link manipulator safe tracking example, investigating the essential properties including safety, smoothness, and robustness against input disturbances under various tunable terms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Tunable Universal Formula for Safety-Critical Control Li, Ming Sun, Zhiyong Koelewijn, Patrick J. W. Weiland, Siep Systems and Control Optimization and Control Sontag's universal formula is a widely used technique for stabilizing control through control Lyapunov functions. Recently, it has been extended to address safety-critical control by incorporating control barrier functions (CBFs). However, deriving a universal formula that satisfies requirements on essential properties, including safety, smoothness, and robustness against input disturbances, 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 term into Sontag's formula. This tunable term enables the regulation of safety-critical control performances, allowing the attainment of desired properties through a proper selection of tunable terms. Generally, the tunable universal formula can be seen as a controller that improves the quadratic program (QP)-synthesized controllers in terms of robustness and smoothness, while also reducing the conservatism (corresponding to robustness) in Sontag's formula. Furthermore, we extend the 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 two-link manipulator safe tracking example, investigating the essential properties including safety, smoothness, and robustness against input disturbances under various tunable terms. |
| title | A Tunable Universal Formula for Safety-Critical Control |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2403.06285 |