On the Necessity of Barrier Certificates

Authors:	Prajna Stephen, California Institute of Technology, United States Rantzer Anders, Lund Institute of Technology, Sweden
Topic:	2.3 Non-Linear Control Systems
Session:	Optimal Control in Nonlinear Systems I
Keywords:	Safety analysis, barrier certificates, density functions, nonlinear systems, convex duality

Abstract

A methodology for safety verification of nonlinear systems usingbarrier certificates has been proposed recently. The conditionwas stated in a sufficiency form: if there exists a barriercertificate, then the system is safe, in the sense that there isno trajectory starting from a given set of initial states thatreaches a given unsafe region. Using theconcepts of convex duality and density functions, in this paper we derive a converse statement forbarrier certificates, showing that in a quite general setting the existenceof a barrier certificate is also necessary for safety.