Detectability And Applications For Several Kinds Of Finite Value Systems

With the rapid development of information technology and system biology,finite value systems(FVSs)are widely used in computer networks,flexible manufacturing systems,gene regulatory networks,and so on.Detectability of FVSs is a vital property of estimating the initial state and current state based on the observable data information,which is particularly important in fault detection and reconfiguration of systems.Using the algebraic state-space representation(ASSR)method,this paper studies the initial detectability(I-detectability)of partially observed discrete event systems(DESs),the detectability of delay Boolean control networks(DBCNs),and the off-line fault detectability of multi logical control networks(MLCNs).Firstly,two concepts of I-detectability of partially observed DESs are given.The observer of the considered system is constructed by using the ASSR method.Based on the observer,two necessary and sufficient conditions of I-detectability are presented for partially observed DESs.Secondly,three concepts of detectability of DBCNs are given and the observer of the extended system is constructed via the ASSR method.According to the observer of the extended system,three necessary and sufficient conditions are proposed for the detectability of DBCNs.Thirdly,the concepts of off-line fault detectability are given and based on the ASSR method,the algebraic forms of normal networks and faulty networks are presented,respectively.By using the iterative matrix algorithm,the matrix of off-line fault detection is constructed.Some necessary and sufficient conditions are obtained for the off-line fault detectability of MLCNs based on the matrix of off-line fault detection.Finally,the obtained results are applied to several concrete models of partially observed DESs,DBCNs,and MLCNs with faults to prove their effectiveness.