On Algebraic Behavioral Analyses of Hybrid Petri Nets

点击翻译按钮获取中文摘要

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.