基于极小T-不变量增加的Petri网可达性分析

Reachability analysis of Petri nets based on minimal T-invariant adding

基于极小T-不变量增加的Petri网的可达性分析,首先对网的状态方程加以合理的约束,求得一组特征解向量;然后利用扩展极小T-不变量关系图和扩展借矩阵在这些特征解向量的基础上适当添加整数倍的极小T-不变量;最后再判断这个添加极小T-不变量后的解向量的可达性。该方法不仅能判定一类含T-不变量Petri网的可达性,而且能在可达的情况下求得一个合法的变迁发生序列,并在一定程度上简化了可达性分析的过程。

The reachability problem of a class of Petri nets can be solved by a method based on minimal T-invariant adding. This approach first gave some reasonable constraint conditions to the fundamental equation of the net,and then obtained some characteristic vectors to solve the linear constrained problem. After that,added some properly minimal T-invariants to the characteristic vectors by using an extended relation graph of minimal T-invariants and an extended borrowing matrix. Finally it was determined whether or not the consequent vector can be transformed to a target state. This method can not only decide whether the target state is reachable,but also find a legal firing transition sequence leading to that state,and make the determination very simple.