Supervisor Synthesis For Discrete Event System Based On Constraint Transformation

Discrete Event System (DES) is a kind of man-made dynamic system, which is driven by the outside event occurrence, such as flexible manufacturing system and workstation, large-scale computer and communication network, air or earth transportation management system and so on. The main research tools of supervisory control of DES are automata, formal language and Petri net. As Petri net has powerful modeling and analysis ability, it is used to study the DES supervisory control when the specifications are described by linear vector constraints.For a system in application, specifications and targets are proposed to make sure that the system can only evolve in some admissible states instead of forbidden states, which are described by the linear vector constraints. The supervisor with only controllable and observable events in DES can be directly achieved through linear vector constraints. However, in the presence of uncontrollable or unobservable events, the specified linear vector constraint may become illegal, which will result in an illegal supervisor. The method to solve this problem is to transform the illegal constraint into legal one, based on which we can obtain the legal supervisor. The supervisory control of Petri net with uncontrollable or unobservable transitions based on constraint transformation is researched in this dissertation, and can be cataloged as follows:Firstly, Generalized Mutual Exclusive Parikh Vector Constraint is introduced, and matrix row transformation is proposed for the constraint transformation in the Petri net with uncontrollable transitions, which can make the illegal constraints into legal ones. Then we prove that "less-than or equal" and "greater-than or equal" hybrid vector constraints can be equivalently transferred into Parikh vector constraints, based on which we can realize the supervisor synthesis of Petri net with uncontrollable or unobservable transitions.Secondly, equations are constructed according to the transformation requirements from illegal constraints into legal ones. The method of generalized inverse matrix is initially introduced to give the transformation solution, based on which legal constraints can be achieved. This method can predict the existence of transformation on the compatibility of the equations, and criterions are given to select the optimal supervisor.Thirdly, local related transition set, local related sequence and increment are proposed for an uncontrollable or unobservable transition, which can define the relationship between the uncontrollable or unobservable transition and its local related transitions, then we can realize the indirect control of the uncontrollable or unobservable transition through controlling its local related transitions. This method can transform the constraint only using the local information of Petri net, thus the complexity of the method will not be affected by the overall scale of the Petri net.Fourthly, the method of supervisor synthesis based on a new subnet called FRSN is initially proposed. The properties and analysis methods of uncontrollable subnet and joint-free subnet are presented. The definition and properties of FRSN are introduced, and an algorithm is provided to create FRSN. Under the condition that the uncontrollable subnet is joint-free, a method is proposed to transform illegal constraints into legal ones on the basis of FRSN.Finally, the state estimation problem of the unobservable transition in a kind of special Petri net—Event Graph is studied, and algorithm based on incident matrix is given to obtain the estimator of the unobservable transition. Observe-cost is analyzed and a method is provided to search the optimal estimator, which can be used to estimate the state-range of the unobservable transition.The supervisory synthesis methods proposed in the dissertation are not only supported by strict theorems and detailed algorithms, but also illustrated through popular-used examples.