Konda, Rohit and Ames, Aaron D. and Coogan, Samuel (2021) Characterizing Safety: Minimal Control Barrier Functions from Scalar Comparison Systems. IEEE Control Systems Letters, 5 (2). pp. 523-528. ISSN 2475-1456. doi:10.1109/lcsys.2020.3003887. https://resolver.caltech.edu/CaltechAUTHORS:20200625-151814838
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Abstract
Verifying set invariance has classical solutions stemming from the seminal work by Nagumo, and defining sets via a smooth barrier function constraint inequality results in computable flow conditions for guaranteeing set invariance. While a majority of these historic results on set invariance consider flow conditions on the boundary, this letter fully characterizes set invariance through minimal barrier functions by directly appealing to a comparison result to define a flow condition over the entire domain of the system. A considerable benefit of this approach is the removal of regularity assumptions of the barrier function. This letter also outlines necessary and sufficient conditions for a valid differential inequality condition, giving the minimum conditions for this type of approach. We also show when minimal barrier functions are necessary and sufficient for set invariance.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2020 IEEE. Manuscript received March 11, 2020; revised May 24, 2020; accepted June 12, 2020. Date of publication June 19, 2020; date of current version July 3, 2020. This work was supported by NSF under Award 1544332 and Award 1749357. | |||||||||
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| Subject Keywords: | Constrained control, Optimization | |||||||||
| Issue or Number: | 2 | |||||||||
| DOI: | 10.1109/lcsys.2020.3003887 | |||||||||
| Record Number: | CaltechAUTHORS:20200625-151814838 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200625-151814838 | |||||||||
| Official Citation: | R. Konda, A. D. Ames and S. Coogan, "Characterizing Safety: Minimal Control Barrier Functions From Scalar Comparison Systems," in IEEE Control Systems Letters, vol. 5, no. 2, pp. 523-528, April 2021, doi: 10.1109/LCSYS.2020.3003887 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 104066 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 26 Jun 2020 14:27 | |||||||||
| Last Modified: | 16 Nov 2021 18:28 |
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