State Estimation And Fault Diagnosis Of Max-plus Automata With Unobservable Events

The problem of state estimation and fault diagnosis for discrete event systems(DES)has been extensively investigated in the past few decades.In general,the output information of the considered system must be given in order to address state estimation and fault diagnosis.Typically,there exist two different kinds of outputs since DES can be described by states and events whereas sensors can be associated to events or states.The corresponding outputs are event observation and state observation.In the case of event observation,events are partitioned into observable and unobservable subsets.For state observation,a subset of states to which the current states of system belong is known.Note that these two outputs can be combined,which means that there may exist event and state observations during the system evolution.In this thesis we consider only event observation.Max-plus automata are significant mathematical tools for modeling timed DES,especially those with synchronized behavior.This thesis first deals with the state estimation problem of a system represented as a max-plus automaton with unobservable events.To the best of our knowledge there is no work for dealing with this problem for timed automata used as modeling formalism in the literature.According to an observed timed sequence,the state estimation problem consists in finding all possible states in which the system may be at the given time instant.We first give the definition of the set of states consistent with an observation at a given time instant.Then we propose iterative algorithms to solve the state estimation problem online and offline respectively.The main idea behind the proposed algorithms originates from the fact that the dynamic behavior of a max-plus automaton can be characterized by its state vector,solution of recurrent equations on words representing the sequence of occurring events.However we cannot solve the problem directly using the state vector and the pseudo-state vector is defined and adapted to cope with this problem.Based on the state estimation approach,a two-step approach is proposed to deal with the problem of fault diagnosis for max-plus automata.In fault diagnosis,under the event-based framework,the set of unobservable events is partitioned two parts,i.e.,the set of fault events modeling the faulty behavior and the set of regular events that,although not observable,do not describe a faulty behavior.Related literature shows that fault diagnosis problem in the event-based framework can always be transformed to an equivalent problem in the statebased framework.Therefore,in the first step,we proposed an algorithm that transforms automaton G(the given system)to G*(real system to be studied)in order to solve the problem of fault diagnosis in a state-based framework.Our algorithm ensures that the generated timed language of G is equal to the generated timed language of G*.In the second step,the state estimation approach is adapted to calculate the states that consistent with an observed timed sequence and a given time instant in G*.Finally,a diagnosis state with respect to fault classes,such as “normal” or “faulty” or “uncertain”,is associated to the observation.In other words,the occurrence of a fault class is determined.