Distributed inversion in timed discrete event systems

Abstract

Abstract. We consider a discrete event system (DES) modeled by a timed automaton with partial state and event observations. We view the system as an input-output system, where the input is a sequence of event lifetimes, and the output is the resulting sequence of events, states, and transition epochs. We consider the problem of extracting event lifetimes (input) from observations of the output trajectory, which we call inversion. We give necessary and sufficient conditions for invertibility, and an algorithm that extracts event lifetimes from any given output observation of an invertible system. We describe a distributed timed DES model based on the prioritized synchronous product of subsystems, and study the inversion problem in this framework. We show that invertibility in the subsystems implies invertibility in the global system. To illustrate our results, we provide an example of a tandem network.