一类混杂Petri网的极大代数模型研究

针对时间事件图(TEG)建模范围窄的问题,提出了一种用来描述制造系统中的离散和连续事件的混杂事件图(HEG).HEG在TEG的基础上引入连续位置和连续变迁.通过构造一个由四个基本函数组合而成的双子代数系统,推导出一组极小代数等式来表示HEG,证明这组等式在极大代数意义下是线性的.这样可以继续采用极大代数方法来研究HEG.实例表明,HEG及其极大代数方法的适用范围比TEG广,可以用来建模制造系统的混杂动态行为.

Study on max-plus algebraic model for hybrid Petri nets

As a timed event graph (TEG) only having narrow modeling range, a hybrid event graph (HEG) was put forward to describe discrete and continuous events in a manufacturing system. Based on TEG, continuous places and transitions were introduced into HEG. By constructing a novel diode consisted of four basic functions, a group of min-plus algebraic equations was deduced to represent one HEG. The group of equations was proved linear under max-plus algebraic framework. Therefore the max-plus algebraic method was continuously used to studying HEG. An illustrative example shows that HEG has more modeling range than TEG, and can model the hybrid dynamic behaviors of a manufacturing system but TEG cannot.