Exact Safety Verification of Hybrid Systems Using Sums-Of-Squares   Representation
  In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares (SOS) relaxation. And a method based on Gauss-Newton refinement and rational vector recovery is deployed to obtain the invariants with rational coefficients, which exactly satisfy the conditions of invariants. Several examples are given to illustrate our algorithm. 
Wang Lin and Min Wu and Zhengfeng Yang and Zhenbing Zeng
cs.SE math.OC