Supervisor Synthesis And Fault Detection Of Discrete Event Systems Using Petri Nets

This thesis focuses on two main problems:supervisory control of discrete event systems and fault detection of discrete event systems.In both cases Petri nets are used as the reference formalism.Solving the problem of supervisory control of a discrete event system modeled by a Petri net consists in designing a supervisor to restrict the system's behavior within a given specification,which may be typically formalized as generalized mutual exclusion constraints.In general,when dealing with Petri nets,there are two types of supervisors:logic-based supervisors and monitor-based supervisors.Compared with the former,monitor-based supervisors have some advantages such as:computational efficiency is higher,execution algorithm is the same as a Petri net and a model of the closed-loop system can be built by standard net composition technique.However,when some transitions of the net are uncontrollable/unobservable,the given constraints usually cannot be directly enforced on the net using monitors.In such a case,we first need to transform the given constraints into admissible ones,then design monitors enforcing the transformed constraints.However,it has been proved that the designed monitor could not be optimal(i.e.,maximally per-missive)for any classes of Petri nets.In Chapter 3 we propose a new constraint transformation method for a class of Petri nets whose unobservable influence subnets are a nets.The designed monitor is structurally optimal,i.e.,it is more permissive than any other monitor-based supervisor enforcing the given constraint.Faults are inevitable in today's complex industrial environment.It is important to develop appropriate techniques for fault detection both in industry and academia.However,most existing techniques in the Petri net framework still suffer the problem of state explosion,namely the number of reachable markings may increase exponentially with the size of the net.To address this problem,we perform fault diagnosis and diagnosability analysis of labeled Petri nets using the notion of basis marking,which allows us to avoid exhaustive enumeration of the set of reachable markings.In more detail,we first propose a Petri net-based diagnoser for the online fault diagnosis of Petri nets.Then we analyse diagnosability of Petri nets in a centralized setting using a special automaton,called F-Verifier.Finally,the basis marking method is extended to a decentralized setting,i.e.,the net system is monitored by a set of sites with their own observation mask.We also introduce the notion of K-codiagnosability.An algorithm is provided to compute the smallest value of K such that the system is K-codiagnosable.