On Algebraic Behavioral Analyses of Hybrid Petri Nets

由离散和连续两个变量构成了一个既包含离散变量又包含连续变量的混合Petri网。与离散网相比，连续网和混合网的行为都非常复杂，从代数的角度对其分析还不够充分。本文首先考虑离散Petri网的状态方程，其中目的状态和初始状态之间的差是固定的，任意触发计数向量(即非负整数解)完全由初等T-不变量和基本特解表示。从初始状态到目的状态的可达性判定是在有界空间和有限过程中用代数方法提出的。其次，将离散Petri网的代数分析方法应用于连续网和混合网，给出了适用于这些网的条件。第三，从只含连续变量的连续系统中获得只含离散变量的离散系统的一种新方法。

A hybrid Petri net containing both discrete and continuous variables is constructed by discrete Petri nets and continuous Petri nets. Comparison with discrete Petri nets, behaviors of both continuous Petri nets and hybrid Petri nets are very complex and have not been analyzed enough from algebraic approach. In this study, first, a state equation for discrete Petri nets is considered, in which the difference between a destination state and an initial state is fixed, and an arbitrary firing count vector (i.e., a nonnegative integer solution) is completely expressed by elementary T-invariants and fundamental particular solutions. Reachability determination from an initial state to a destination state is algebraically proposed in the bounded space and within finite procedures. Secondly, algebraic analytical approaches of discrete Petri nets are applied to continuous Petri nets and hybrid Petri nets and conditions for applicability to those nets are shown. Thirdly, a novel method for obtaining a discrete system containing only discrete variables from a continuous system with only continuous variables.