基于约束转换的Petri网最优监控器设计

Optimal Petri-net supervisor synthesis based on the constraint transformation

针对不可控影响子网为后向无同步前向无冲突网的广义互斥约束,给出基于约束转换的最优监控方法:根据路径代数法研究后向无同步前向无冲突网的结构,得到与可达性分析相关的若干性质;其次,根据这些性质得到约束转换算法,它将给定约束等价转换为一组"逻辑或"的允许的广义互斥约束;根据允许约束的性质,得到允许监控器存在性的充要条件和最大允许状态反馈控制策略的表达式,分析结果表明,该策略的在线计算能够在多项式时间内完成,及它能够满足实时性的要求;利用一个制造系统的实例演示了该监控方法.

The optimal supervisor synthesis approach is proposed for a class of generalized mutual exclusion constraints （GMECs） on Petri nets where the influence uncontrollable subnets are backward concurrent and forward conflict free （BCFCF） nets. Firstly, the net structure of BCFCF nets is studied by the path algebra approach. Then, several properties about reachability analysis are given. Secondly, a constraint transformation algorithm, by which a given GMEC can be equivalently transformed into a disjunctive of admissible GMECs, is designed based on these properties. Thirdly, these calculated admissible constraints are utilized to derive the necessary and sufficient condition of the existence of any admissible supervisor and the expression of the maximally permissive control policy. The on-line calculation of this control policy can be completed within polynomial times, so it can meet the real time requirement. Lastly, the theoretic re- sults are illustrated by a manufacturing system.