基于不变量综合离散事件系统Petri网控制器

Synthesis of petri net controllers for discrete event systems based on invariant

基于Petri网模型,研究在具有不可控变迁的离散事件动态系统中实现一组不等式约束控制规范的Petri网控制器的存在性及其综合问题.利用系统的关联矩阵,把Petri网控制器的参数阵与受控系统的一个P-不变量用线性方程组联系起来.提出了Petri网控制器存在的代数判据.通过以此方程组为约束条件的一个整数线性规划问题的解,给出了Petri网控制器的结构参数(弧权值)和控制位置的初始标记数.给出的控制器的结构具有极小性.在结构一定的条件下,它是极大允许的.

Based on petri net models of discrete event systems with uncontrollable transitions, the existence and synthesis problems of petri net controllers which realize a set of general linear constraints are studied. By using the incidence matrix of the system, the incidence matrix of petri net controller and control-place invariants are linked together by a set of linear equitions. An algebraic criterion for the existence of the petri net controller is presented. The structural parameters of the petri net controller and the number of initial tokens in control places are determined by the linear equation solution. The proposed controller is with the minimal structure. When the controller structure is given, the controller is maximal permissive.