Design Of Petri Net Monitor Based On Network Structure Compression Technology

Discrete event systems were proposed in comparing with continuous variablesystems. They can represent high-performance man-made systems with thecharacterization of the modern civilization, such as flexible manufacturing systems, data network exchange systems, traffic dispatching systems, automatic vehicle guidedsystems, C3I military command systems and so on. Their state evolutions are drivenby a sequence of events with irregular time intervals. The Petri-net supervisorycontrol is to appropriately forbid events to make the plant obey the important controlspecifications that include the safty, sequential and so on. If there exist uncontrollabletransitions in the plant net, then we cannot design the monitor place for a givenconstraint until this constraint is transformed into an admissible one. However, thistransformation is very difficult since the state space of the uncontrollable subnet mayexponentially grow.In this paper, the aim is to deal with the above mentioned computationalcomplexity problem caused by uncontrollable transitions. Based on the net structurecompressing technology, an appoach is proposed to equivalently simplify an origialcontrol problem as a new one with a smaller plant net and a simper constraint. It issummarized as follows:(1) Several methods are proposed to compress some areas of theuncontrollable subnet, which should be in the conflict structure, synchronizationstructure and forward synchronization free structure, respectively, into a singleplace.(2) The methods are proposed to equivalently transform the originallinear constraint into a new one on the new net.(3) Based on the above methods, an algorithm is obtained to compress theoriginal net and to equivalently transform the original constraint.Since this approach can be used to effectively compress the plant net, it is efficientto reduce the state space. Consequentley, it is useful to reduce the computationalcomplexity in the supervisor synthesis. If the uncontrollable subnet is a state machine,this approach can be used to transform the original constraint into an admissible one, whose monitor place can be designed, and consequently, the high computationalcomplexity problem is well solved. In addition, this approch is illustrated by severalreal discrete event systems including a flexible manufacturing system, and a trafficdispatching system. The advantages are also shown by comparing it with othermethods.