基于矩阵方法的有界Petri网系统的能观性分析

Observability analysis of bounded petri net systems via a matrix approach

Petri网和有限自动机是离散事件动态系统的两类主要研究内容.而Petri网系统的能观性分析与判别是基于Petri网的实际系统设计、优化、监测及控制的重要基础.以往关于Petri网能观测性的研究缺乏定量化的充要判别条件.本文利用代数矩阵方法研究了带有输出的有界Petri网系统的能观性问题.首先,基于矩阵的半张量积,将带有输出的有界Petri网系统的动态行为以线性方程组的形式建立了数学模型.然后,针对初始标识和当前标识,介绍了两种能观性定义.最后,基于矩阵运算建立了关于有界Petri网系统能观性的几个充分必要条件,并给出严格证明.数值算例验证了理论结果.本文提出的方法实现了有界Petri网系统能观性的矩阵运算,易于计算机实现.

Petri nets and finite automata are two main kinds of research contents in discrete event dynamic systems.The observability analysis and judgement of Petri nets are essential for the design,optimization,monitoring and control of actual systems,but quantitative necessary and sufficient conditions for observability are inexistent during existing research literature.This study investigates the observability problem of bounded petri net systems with outputs via a matrix approach.Firstly,several different petri nets with outputs are introduced.Secondly,using semi-tensor product of matrices,the mathematical modeling of dynamical behavior of bounded petri net systems with outputs is established in the form of linear equations.Thirdly,two different observability definitions,either for initial marking or current marking,are introduced.Finally,some matrix-form necessary and sufficient conditions for both the initial and current marking are first proposed.The proposed approach realizes the matrix operation for the observability of bounded petri net systems and it can be realized easily by computer.