Diagnosability of Vector Discrete-Event Systems Using Predicates

The diagnosability problem of faults is studied in the framework of vector discrete-event system (VDES). A VDES is a discrete-event system model in which a system state is represented by a vector with integer components, and state transitions are represented by integer vector addition. Predicates are employed to verify the fault diagnosability of VDES, since, defined as functions, predicates can conveniently identify particular state sets of interests. Specifically, system states are partitioned into different subsets by predicates, and the fault diagnosability of a system is verified by checking a subset of states. A sufficient condition for fault diagnosability of VDES is presented first. A necessary and sufficient condition is then developed. According to the two conditions, two types of predicates are given to partition the states in a VDES. In this work, a diagnoser or a full state enumeration is not constructed, whose complexity is exponential with respect to the system state size. In order to verify whether a system satisfies the proposed conditions, several polynomial algorithms and an algorithm by constructing a tree automaton are developed. Several examples are provided to illustrate the results obtained in this paper.