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Prajna, Stephen, and Ali
Jadbabaie. "Safety verification of hybrid systems using barrier certificates." International Workshop on Hybrid Systems: Computation and Control. Springer, Berlin, Heidelberg, 2004.
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Marcel, Menner; Eugene, Lavretsky. "Translation of Nagumo's
Foundational Work on Barrier Functions: On the Location of Integral Curves of Ordinary Differential Equations".
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There are several different types of barrier functions. One distinguishing factor is the behavior of the barrier function at the boundary of the forward invariant set
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for stability. For every ordinary differential equation that robustly fulfills a safety property of a certain type there is a corresponding barrier certificate.
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Maghenem, M., Sanfelice, R. G. (February 2021). "Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions".
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Stefan
Ratschan: "Converse Theorems for Safety and Barrier Certificates". IEEE Trans. on Automatic Control, Volume 63, Issue 8, 2018
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This article is about the topic in dynamical systems. For the topic in constrained optimization, see
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Ames, A. D., Coogan, S., Egerstedt, M., Notomista, G., Sreenath, K., Tabuada, P. (2019),
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in 1942. The term "barrier certificate" was introduced later based on similar concept in
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A barrier function that goes to infinity as the inputs approach the boundary of
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Barrier certificates play the analogical role for safety to the role of
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Prajna, S., Jadbabaie, A. (2004), Alur, R., Pappas, G. J. (eds.),
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Ames, A. D., Xu, X., Grizzle, J. W., Tabuada, P. (August 2017).
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Safety
Verification of Hybrid Systems Using Barrier Certificates
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The first result in the field of barrier certificates was the
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Showing that a set is forward invariant is an aspect of
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may be too technical for most readers to understand
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