DISTRIBUTED INVERSION IN TIMED DISCRETE-EVENT SYSTEMS

We consider a discrete event system (DES) modeled by a timed automaton with partial state and event observations. We view the system as an i nput-output system, where the input is a sequence of event lifetimes, and the output is the resulting sequence of events, states, and transi tion epochs. We consider the problem of extracting event lifetimes (in put) from observations of the output trajectory, which we call inversi on. We give necessary and sufficient conditions for invertibility, and an algorithm that extracts event lifetimes from any given output obse rvation of an invertible system. We describe a distributed timed DES m odel based on the prioritized synchronous product of subsystems, and s tudy the inversion problem in this framework. We show that invertibili ty in the subsystems implies invertibility in the global system. To il lustrate our results, we provide an example of a tandem network.