Safety Verification of Hybrid Systems Using Barrier Certificates

By Stephen Prajna, Ali Jadbabaie. International Conference on Hybrid Systems: Computation and Control, 2004

751 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d451245c0d1a89bdf2977ec04fa4551ac981e18d

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Citations in the corpus

Formal verification of hybrid systems (2011, background): “We will informally explain the first such notion, called barrier certificates [47,48].”
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates (2007, background): “More examples can be found in [36], [37].”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, neutral): “difficult in general, but algorithms for restricted classes of dynamics do exist; for example, dynamics which are piecewise linear [35], are linear with sector bounded nonlinearities [36] or are piecewise polynomial [37].”
Control Barrier Functions for Systems with High Relative Degree (2019, neutral): “, to prove set invariance [4][15][16][21] and for multi-objective control [14].”
Control Barrier Functions: Theory and Applications (2019, positive): “Barrier certificates were introduced as a convenient tool to formally prove safety of nonlinear and hybrid systems [9], [10]; these results, again, seemed to independently discover Nagumo’s theorem.”
Control barrier function based quadratic programs with application to adaptive cruise control (2014, methodology): “Motivated by [19] and [23], we first present a novel reformulation of barrier functions, in a manner that is analogous (yet reciprocal) to how Lyapunov functions are used to establish exponential stability.”
Set Propagation Techniques for Reachability Analysis (2021, neutral): “Barrier certificates can also be used to provide an over-approximation of the reachable set using the zero sublevel set of a function [28].”
A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems (2017, background): “a safe region in the state space and a control policy to remain inside it; a related approach involves ensuring invariance through “barrier functions” [24], [25].”
A tutorial on sum of squares techniques for systems analysis (2005, background): “Theorem 22 ([40]): Let the hybrid system H = (X , L,X0, I, F, T ) and the unsafe set Xu be given.”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, background): “A further possibility to verify that there exists no trajectory from a set of initial states to a set of unsafe states is the use of barrier certificates [137, 138].”