A heuristical method for safety verification of nonlinear continuous systems
Wang Li, Lu Yang, Wensheng Yu · 2017
Hybrid system is an important mathematical model for Cyber-Physical System, many physical process always modeled by differential equations. The safety verification of those systems become an urgent problem. In this paper we proposed a heuristical method to determine the system defined by nonlinear differential equation is whether safe or not, we consider the Van der Pol equation as a case study to illustrate this method. Moreover, we consider the problem of searching the barrier functions when the corresponding un-safety region enlarge, we figure out when the radius of the un-safety region is 1.2082 the system is safe. on the other side, from the point of reachablity analysis, we proved when the radius of the un-safety region enlarge to 1.209, the system become unsafe. By using this method, we consider the safety verification problem with specified precision with the radius of the unsafe region.