Petri nets decomposition and its application in performance evaluation and control of dynamic systems

A new Petri Net decomposition methodology is proposed. The new methodology overcomes the computational limitations associated with large scale Petri Nets, thereby making Petri Nets a more practical tool for analysis of dynamic systems. The methodology decomposes the Petri Net into a set of subnets where performance of each subnet is evaluated and the results are aggregated to identify the performance of the Petri Net. A subnet consists of one or more correlated subnets. A correlated subnet is the smallest subnet of the Petri Net where transitions can fire without hindrance from the rest of the systems operations. This property is called semi-independence or near-independence. Hence, a subnet can operate semi-independently if it consists of correlated subnets. A group of (one or more) correlated subnets is augmented with an appropriate boundary net to assure consistency between results obtained from the analysis of the groups of correlated subnets and those obtained from analysis of the whole Petri Net. Procedures for identifying the correlated subnets, for aggregating correlated subnets into efficient groups of subnets and for developing a boundary net and its parameters for a group of correlated subnets are developed. Each transition in a Petri Net is represented by a logical IF…, THEN… rule, and the system\u27s dynamics is represented by a weighted rule set since the Petri Net\u27s dynamics are governed by the firing of its transitions. The rule weights represent the firing probability of the rules. Systematic procedures for extracting the rule set and determining the rule weights are developed. Examples show that performance evaluation of a large scale Petri Net through simulation of its rule set is markedly much more efficient than through existing Petri Net solution methodologies. Deadlock issues of dynamic systems are analyzed through simulation of the system rule set. The procedures for identifying the smallest subnet whose deadlock will results in the Petri Net being in the state of deadlock or partial-deadlock are proposed. In addition, a methodology for parallel simulation of a Petri Net using the rule set concept is developed. Finally, an example to control a dynamic system through a fuzzy logic controller in conjunction with the system\u27s rule set is presented