基于多面体包含的非线性混成系统可达性分析

摘要

针对一类非线性混成系统的可达性问题,提出了一种基于多面体包含的分析方法.首先介绍了混成系统及其可达性,讨论了如何应用多面体包含对多项式混成系统进行线性近似,并采用量词消去和非线性优化方法来构造相应的线性混成系统,然后运用验证工具SpaceEx求得原非线性混成系统的过近似可达集,并应用于验证系统的安全性.%To study the reachability of a class of nonlinear hybrid systems, this paper presented an verification method based on polyhedron inclusion. Firstly, some notions about hybrid systems and reachability were introduced. The method based on polyhedron inclusion was proposed to compute the linear approximation of polynomial hybrid systems. Quantifier elimination and nonlinear optimization method were applied to obtain the associated linear hybrid systems. Then the over-approximation of reachable set of original polynomial hybrid systems can be computed by using SpaceEx. Furthermore, the safety properties of the systems also can be verified.