Symbolic Reachability Analysis of Hybrid Systems

Abstract

定义了一种称作混合区域的形式化结构表示矩形混合系统的状态集,它实际上是由一组特殊形式的线性不等式联立表示的多面体空间.证明了混合区域对于矩形混合系统的可达性操作的封闭性.此外,用矩形混合系统近似模拟非线性混合系统,相应地解决了非线性混合系统的可达性问题.使用混合区域,可以直接计算由某个正则的混合区域开始的可达集,这样,混合系统的可达性问题主要是求解混合区域的正则型问题,而这问题是一种线性规划问题,可以使用经典的线性规划算法加以解决.;A restricted constraint system called hybrid zone is formalized for the representation and manipulation of rectangular automata state-spaces. Hybrid zones are proved to be closed over reachability operations of rectangular hybrid systems. In addition, rectangular hybrid systems are used to simulate nonlinear hybrid systems, which enables us to use hybrid zones for reachability analysis of nonlinear hybrid systems. After the hybrid zone has been converted to the canonical form, reachability operations for hybrid systems can be implemented straightforwardly. Hence, the main computation is the operation for obtaining the canonical form of hybrid zones. Finding the canonical form can be automated by an algorithm for linear programming.