On Algebraic Behavioral Analyses of Hybrid Petri Nets

由离散Petri网和连续Petri网构成了一个同时包含离散和连续变量的混合Petri网。与离散Petri网相比，连续Petri网和混合Petri网的行为都非常复杂，从代数的角度分析还不够。在这项研究中，首先，考虑离散Petri网的状态方程，其中目的地状态和初始状态之间的差异是固定的，并且任意触发计数向量（即，一个非负整数解）完全由初等T-不变量和基本特解表示。代数地提出了在有界空间和有限过程内从初始状态到目标状态的可达性判定。其次，离散Petri网的代数分析方法被应用到连续Petri网和混合Petri网和适用于这些网的条件。第三，一种新的方法，从一个只有连续变量的连续系统获得一个只有离散变量的离散系统。

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.