Supervisory Control Of Discrete Event Systems With Partial Observation Based On State-Tree Structures

Over the past decades,the discrete-event systems(DES)are well developed,which are re-lated to a wide range of application domains.Typical examples can be found in manufac-turing systems,traffic systems,database management systems,communication protocols,and logistic(service)systems.With such various disciplines,there is no doubt that a lot of researchers and engineers are interested in modelling,synthesizing,and controlling the DES.In order to formulate the various control problems,Ramadge and Wonham(RW)in-troduce the supervisory control theory(SCT)for a general class of DES.In view of the RW framework,a DES is modeled as an automaton and its dynamics are described by a for-mal language generated by the automaton over an alphabet of event labels.To control the system,a controller is constructed so that the controllable events are enabled/disabled in a proper way,which is also called a supervisor.However,for some complex systems,the state explosion problems are long-standing issues in the synthesis of the controllers.As an extension to SCT,a new framework,state-tree structures(STS),has been deployed to manage the state explosion problem of the supervi-sory control of DES(SCDES).Naturally equipped with vertical and horizontal structures that are realized by state-trees and holons,systems with large state size can be modeled and controlled in STS.The most important advantage of the STS is that for a control prob-lem,although both approaches in the RW framework and STS generate the same controlled behavior,the one in STS is more computationally efficient.In reality,only a subset of the event labels can actually be observed due to the limited actu-ating and sensing capabilities of the systems.In SCT,the supervisory control problem has been well studied under partial observation,and various approaches have been proposed to find the observable supervisors.However,for complex systems,the state explosion prob-lems remain to be managed.This dissertation aims to address this notorious issue of the supervisory control with partial observation in the STS framework.The main results are shown as follows.1.First,owing to the observability of events,we define the natural projection with re-spect to STS.Initially,the natural projection is defined on the basis of the predicate,which represents a set of state-trees,with respect to the observability of events.Ac-cordingly,the transition function is revised as a predicate transformer between pro-jected predicates via strings(composed of a set of observable events).The soundness of the projected transition function is proved,which shows the reasonability of the definition.Moreover,propositions are proposed to show that the natural projection does not change the dynamics of the system over observable events.With this def-inition,the computational cost is much reduced to acquire the natural projection in STS.Thus,we can analyse the supervisory control problems with partial observation further,especially for complex systems.2.Second,to address the supervisory control problems with partial observation,we pro-pose supremal normal subpredicates in the STS framework.It is realized by the following two steps.First,for a specification represented by a predicate,a supre-mal normal subpredicate,which requires only the controllable-observable events to be enabled/disabled,is computed.Second,according to the new transition function constructed by projecting out the unobservable events,the supremal weakly control-lable and coreachable subpredicate is obtained with respect to the supremal normal subpredicate.This proposed approach based on STS provides the possibility to su-pervise controllable events under partial observation in large-scale systems with the state explosion problem managed.Moreover,in order to demonstrate the industrial applications of the contribution of this research,three examples are addressed.3.Third,to solve the supervisory control problems with partial observation,we propose an observable subpredicate under a less constrictive condition compared with normal-ity.The work is initiated on the normal STS framework,requiring that for any two subpredicates whose conjunction is false,the conjunction of their projected subpred-icates should also be false.First,following the definition of the observability based on STS,it is proved that there does not exist the supremal observable subpredicate.Second,we construct a subclass of observable subpredicates of a given predicate(ob-tained by a specification)with normal STS in consideration.Third,with the existence of a largest element in the subclass,a weakly controllable,coreachable,and observ-able(WCCO)subpredicate is computed to solve the supervisory control problem of the normal STS by an iterative algorithm.An illustrative example with state size over 1012 is given to show that the proposed algorithm based on STS is superior to the approach based on SCT,which leads to the program crashes in SCT.