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Characterizing Safety: Minimal Control Barrier Functions from Scalar Comparison Systems

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. 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/lcsys.2020.3003887DOIArticle
https://arxiv.org/abs/1908.09323arXivDiscussion Paper
ORCID:
AuthorORCID
Konda, Rohit0000-0002-0423-5531
Ames, Aaron D.0000-0003-0848-3177
Coogan, Samuel0000-0003-0495-1535
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.
Funders:
Funding AgencyGrant Number
NSFCNS-1544332
NSFECCS-1749357
Subject Keywords:Constrained control, Optimization
Issue or Number:2
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:07 Jul 2020 22:29

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