Decentralized prognosis of failures in discrete event systems

Abstract

We study the prognosis of failures, i.e., their prediction prior to their occurrence, in discrete event systems in a decentralized setting where multiple prognosers use their local observations to issue local prognosis decisions. We define the notion of correctness of a decentralized set of prognosers in terms of ldquono missed detectionsrdquo (each failure is prognosed prior to its occurrence) and ldquono false alarmsrdquo (an incorrect prognostic decision is never issued), and introduce the notion of coprognosability as an existence condition. When specialized to the centralized case (i.e., the case of a single prognoser), this condition turns out to be weaker than the one introduced in (S. Gene and Sl Lafortune, 2006) since a uniform bound on the number of steps within which a failure will occur is not required. For comparison we also introduce the stronger notion of ldquouniformly bounded coprognosabilityrdquo and identify the subclass of decentralized prognosers for which it serves as an existence condition. We show that the two notions coincide when the underlying system and its nonfailure specification possess finite-state representations, and present a verification algorithm. We also introduce the notion of reaction bound for coprognosis as the earliest time beyond a prognostic decision when a failure can occur, and present an algorithm for computing it. An algorithm is also presented for an online prognosis of failures. We show that the notions of coprognosability and its uniformly bounded version are in general incomparable with the notion of codiagnosability (that guarantees a uniformly bounded delay detection of a failure by a local diagnoser). When the system cannot execute an unbounded sequence of unobservable events, uniformly bounded coprognosability implies codiagnosability, whereas coprognosability and codiagnosability remain incomparable.