局部公平网的充要条件研究

A sufficient and necessary condition for local-fair Petri nets

Petri的局部公平性反映了网系统在局部行为的公平关系,给出了局部公平Petri网的一个充要条件,即如果Petri网具有若干个互不相交的变迁不变式的支撑,则该网是为变迁不变式覆盖的.同时提出了状态观测器的概念,根据网的库所不变式理论,通过把网中所有的状态观测器设计为一个库所不变式,可把一个局部公平网设计为一个公平网.最后给出了状态观测器初始标志的确定方法,来最大限度地保证网系统的行为不受观测器的约束.

Localfairness of Petri nets is the representation of locally fair relations of the net systems behavior. Presented in this paper is a sufficient and necessary condition for localfair Petri nets, which is the Petri net covered by Tinvariants that are mutually disjoint. The concept of state observer is also proposed that, based on Pinvariants of nets, can be utilized to design a fair net from a localfair net via enforcing all state observers added to be a Pinvariant. Also a method is developed to determine the initial tokens for the state observers, which can ensure that the behavior of a fair net is maximally permissive. Finally, the results obtained are illustrated by an example arising from flexible manufacturing systems.