有界Petri网系统稳定性与镇定性分析的矩阵半张量积方法  

Semi-tensor product of matrices approach to stability and stabilization analysis of bounded Petri net systems

作　　者：韩晓光[1,2] 陈增强[1,2,3] 刘忠信[1] 张青[3] 

机构地区：[1]南开大学计算机与控制工程学院,天津300350 [2]南开大学天津市智能机器人技术重点实验室,天津300350 [3]中国民航大学理学院,天津300300

出　　处：《中国科学：信息科学》2016年第11期1542-1554,共13页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:61573199;61573200);天津市自然科学基金(批准号:14JCYBJC18700;13JCYBJC17400)资助项目

摘　　要：基于矩阵半张量积(semi-tensor product,STP)方法,本文研究了有界Petri网系统稳定性和镇定性问题.首先,在布尔代数框架下,对先前所建立的有界Petri网系统的标识演化方程进行了改进.利用改进后的这个方程,给出了有界Petri网系统平衡点稳定性判别的充要条件.其次,为了研究有界Petri网系统的标识反馈镇定问题,定义了Petri网系统的标识k步前可达性集,并给出了它的一些基本性质.利用这些性质,给出了有界Petri网系统镇定性的判别方法,并设计了最优标识反馈控制器的有效算法.本文的结果是基于矩阵形式的,利用MATLAB的STP工具箱,可将Petri网系统的稳定性和镇定性判别问题转化为简单直接的矩阵计算问题.该方法的优势不仅在于所得到的结果形式简单,而且易于计算机实现.最后,实例说明了该方法的可行性和有效性.In this paper,we investigate the problems of stability and stabilization for bounded Petri net systems（BPNSs） by using the semi-tensor product（STP） of matrices.First,a new matrix equation,under the framework of Boolean algebra,is established,and is based on our previous results presented on the marking evolution equation of BPNSs.This equation made it possible to provide the necessary and sufficient condition for the equilibrium point stability of BPNSs.Second,the problem associated with marking feedback stabilizability is solved by introducing the concept and some properties of the marking pre-reachability set of BPNSs,respectively.By resorting to these properties,the necessary and sufficient condition for equilibrium point stabilization is presented.In addition,a design procedure is proposed to find all the optimal marking feedback controllers that implement the minimal length trajectories from each marking to the equilibrium point.The proposed results,in this paper,are based on the matrix form,thus the problems of verifying the stability and stabilization of BPNSs are expressed in the matrix computation.This is very simple and straightforward work by means of the MATLAB toolbox of the STP of matrices.The proposed results are of a very simple form and can conveniently be implemented on a computer.Finally,several examples are presented to illustrate the validity and application of the proposed approaches.

关 键 词：PETRI网 离散事件动态系统 矩阵的半张量积 平衡点 稳定性 镇定性 

分 类 号：TP301.1[自动化与计算机技术—计算机系统结构]