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A Two-Step Approach for Fault Diagnosis of Max-Plus Automata

In this paper, a two-step approach for on-line fault diagnosis of timed discrete event systems modeled with max-plus automata is presented. The set of events is divided into two disjoint subsets, i.e., observable and unobservable subsets, and failures are associated to unobservable ones. Once a sequence of pairs (event, time-instant) is observed, the fault diagnosis problem consists in detecting an abnormality of the system evolution and isolating the source of this abnormality. For a max-plus automaton, we first propose an algorithm to build its augmented version whose states are partitioned into two disjoint parts, the normal part and the faulty part, with respect to a given fault class. Then we prove that solving fault diagnosis of the original automaton is equivalent to estimating the states of the augmented automaton. Finally, an algorithm is proposed to summarize how to perform on-line fault diagnosis using a state estimation based approach.