An efficient framework for barrier certificate generation of uncertain nonlinear hybrid systems

Due to the ability to handle uncertain nonlinear hybrid systems, barrier certificate based method has been widely used in safety verification problem. In this paper, an efficient framework, combining sum of squares programming with interval analysis, is proposed to generate barrier certificates for uncertain nonlinear hybrid systems. It utilizes the feature of bounded uncertainties to get a deterministic hybrid system, whose barrier certificates can be efficiently computed using sum of squares programming. The computed barrier certificates are then chosen as candidate barrier certificates for the original uncertain hybrid system, and need to be checked the satisfaction of the associated barrier certificate conditions, via an interval analysis based method. As an application, our approach is used to verify safety properties of non-polynomial hybrid systems. Some experimental results are given to show the efficiency of our approach.