A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates

By Stephen Prajna, Ali Jadbabaie, George Pappas. IEEE Transactions on Automatic Control, 2007

726 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Safety, Risk, Reliability and Quality, Software

View Paper: https://www.semanticscholar.org/paper/43b4d23f0223f1f023e5db155293517a9ba7e075

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Magnus Egerstedt
2. Calin A. Belta
3. Wei Xiao
4. Paulo Tabuada
5. Aaron D. Ames
6. Samuel D. Coogan
7. Koushil Sreenath
8. Rajeev Alur

In Safety, Risk, Reliability and Quality

1. Magnus Egerstedt
2. Paulo Tabuada
3. Xiangru Xu
4. Li Wang
5. Aaron D. Ames
6. Jessy W. Grizzle

In Software

1. Magnus Egerstedt
2. Rajeev Alur
3. Calin A. Belta
4. Paulo Tabuada
5. Matthias Althoff
6. Xiangru Xu
7. Li Wang
8. Aaron D. Ames

Citations in the corpus

• Control barrier function based quadratic programs with application to adaptive cruise control (2014, background): “Barrier functions—first utilized in optimization [7]—are now common throughout the control and verification literature due to their natural relationship with Lyapunovlike functions [23], [27], their ability to provably establish invariance of sets [6], [19], [20], [28], and their relationship to mul”
• Control Barrier Functions: Theory and Applications (2019, background): “Importantly, the necessity of barrier certificates were studied [11] along with their extension to a stochastic setting [12].”
• Robustness of Control Barrier Functions for Safety Critical Control (2016, background): “Recall that the original barrier condition in Prajna et al. (2007) requires that ḣ ≥ 0, when expressed in the notation of the present paper, which implies that all superlevel sets of h inside C are invariant.”
• Safety Barrier Certificates for Collisions-Free Multirobot Systems (2017, methodology): “Barrier certificates were used for safety verification of dynamical systems [13].”
• Formal verification of hybrid systems (2011, background): “We will informally explain the first such notion, called barrier certificates [47,48].”
• Control Barrier Functions for Systems with High Relative Degree (2019, background): “, to prove set invariance [4][14][18] and for multi-objective control [13].”
• Control Barrier Function Based Quadratic Programs for Safety Critical Systems (2016, positive): “…are now common throughout the control and verification literature due to their natural relationship with Lyapunov-like functions [5], [6], their ability to establish safety, avoidance, or eventuality properties [7], [8], [9], [10], [11], and their relationship to multi-objective control [12].”
• Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, background): “To the best knowledge of the author, upper bounds have only been computed by barrier certificates so far [139].”