Supervisory Control For Discrete Event Systems Based On Cascade Petri Net

Due to the rapid development of computer science and its extensively application in modern society, some scholars found a new type of dynamic systems named as discrete event systems (DES), which is different from continuous variable dynamic systems. The dominating characteristic of DES is that its evolution is not driven by times but events. Essentially, DES is a manmade system. The typical DES includes the manufacturing system (especially FMS and CIMS), system scheduling, communication network, traffic control system, random service system and computer operating system and so on. The research aim of DES is two-fold: one is to provide tools for performance analysis, the other is to offer supervisory control methods for DES.The present dissertation mainly studies the supervisory control of DES, namely, how to design a controller for a DES plant such that its closed-loop behaviors satisfying a desirable specification. In contrast to automaton/formal language model, Petri net model has advantages such as the capability of handling of concurrence, the graphic representation of controlled plants and the high computation efficiency etc. Hence, Petri net is taken as a mathematical tool to study the control theory of DES here.The principal research results and contents are composed by two interdependent parts, namely, the Petri net theory part and the supervisory control part, where the latter is based on the former.The Petri net theory part: Firstly, a new subclass of Petri net named as cascade Petri net, which is the superset of acyclic Petri net, is formally defined. Secondly, some fundamental properties and some methods of reachability analysis of cascade Petri net are presented in detail. Finally, the determinant and decomposition algorithms of cascade Petri net are given. After all, the research results on cascade Petri net are an extension of the arisen Petri net theory, which can not only be used for designing controllers of DES, but also be used for analyzing reachability of Petri nets.The supervisory control part: Firstly, the existence condition of maximally permissive multi-valued logic controller for the forbidden state problem is presented. Then, the four procedures of controller synthesis, namely, the constraint transformation method (CTM), the eigen marking method (EMM), the linear integer program method (LIP) and the extended linear integer program method (ELIP) are discussed one by one. The CTM is suitable for the case that all E-type influentially uncontrollable subnets are state graphs, and the outstanding virtue is that thedesigned controller is explicit. The EMM is suitable for the case that all F-type influentially uncontrollable subnets are normalized cascade Petri nets, and the advantage is that control patterns can be on-line computed within polynomial times. The LIP is suitable for the case that the uncontrollable subnet is cascade Petri net and all cascade subnets are either acyclic Petri nets or state graphs, and control laws can be calculated using some standardized mathematical tools. The ELIP is suitable for the case that the uncontrollable subnet is cascade Petri net and some cascade subnets are neither acyclic Petri nets nor state graphs, and the main character is that the nonlinear integer program problem is converted into the problem that can be solved by using some standardized mathematical tools.All conclusions and algorithms in this dissertation are obtained via strictly theory proof. Many examples are provided throughout the text to verify and illustrate the efficiency and feasibility of the theorems and algorithms.