Research On Transformation Algorithms Of Generalized Mutual Exclusion Constraints Based On Petri Nets

A discrete event system(DES)is a dynamic system driven by events rather than time.Similar to continuous time systems,discrete event systems also need to limit the state of the system in order to meet the expectation.The state that does not meet the expected requirement,s is a forbidden state,such as the collision of the vehicle in an AGV system,the deadlock in a flexible manufacturing system,etc..The forbidden state monitoring is to design supervisory controller for the discrete event system so that the closed-loop system will never reach a forbidden state.Although automaton,form language and some other tools can be used to study the supervisory control problems of the discrete event system,we choose Petri nets as the modeling tool to study the supervisory control problems of the discrete event systems with Generalized Mutual Exclusion Constraints(GMECs),considering the advantages of Petri nets in describing the system states and concurrent situation.There already exist some effective approaches to design supervisory controllers in the case that all transitions in the Petri net are controllable.However,in the case of uncontrollable transitions existing in the Petri net,the monitoring problem becomes complicated and difficult due to the possibility that the legal markings may reach the forbidden markings by firing some uncontrollable transitions.The focus of this pa-per is to transform the initial GMECs with uncontrollable transitions into the maximal admissible ones.As a result,the legal markings represented by the transformed con-straint will never reach the forbidden markings by firing the uncontrollable transitions only.Thus,the transformation makes the supervisor design much easier.The main work of this paper is summarized as follows:1.Considering the situation that the uncontrollable subnet of the object Petri net to be enforced on GMECs is an FSFCF net,we put forward the concept of,"the branches of a place" for the first time to analyze the flow direction of the tokens in the place with multiple output transitions and the influence of such a structure on the GMECs.Based on of the structure of the FSFCF net,we classify the places in the uncontrollable influence subnet.Then,by analysing the properties of different structures of the FSFCF net,we obtain the virtual weights of different types of places.Finally,the initial GMECs are transformed into the maximal admissible constraints.2.Considering the case that the uncontrollable subnet of the object Petri net to be enforced on GMECs includes the circle and the places with multiple output tran-sitions.For the first time,the concept of "the layer of the Petri net" is put forward to layer the places in the uncontrollable subnet.What's more,the concept of the increment function,the maximum increment function and the maximum total function are extended to analyze the influence of uncontrollable transitions on the system state and show the influence in the GMECs.Then,in accordance with the order from the bottom up,the maximum increment function of each place in each layer in the subnet is analyzed.Finally,we transform the initial GMECs into the maximum admissible ones.We also use some examples to illustrate the two transformation algorithms.