Algebraic construction of diagnosers for unobservable events in finite state automaton using the STP method

This paper addresses the diagnosis of Discrete Event Systems (DES) with unobservable events by proposing an algebraic construction method for a diagnoser using the Semi-Tensor Product (STP) of matrices. We first define diagnosability for the single unobservable event scenario and construct a diagnostic automaton to identify the event's occurrence. The diagnostic automaton is then integrated with the original system automaton via parallel composition, making unobservable event transitions explicit. STP theory is used to algebraically model the composed automaton, unifying state evolution, event transitions, and ϵ-closure computation into matrix operations, forming an implementable algorithm. Numerical examples demonstrate the method’s effectiveness in deterministic settings, and its adaptability to nondeterministic automata, multiple unobservable events, and probabilistic disturbances is discussed. The results highlight the STP-based framework's potential for fault diagnosis in DES.