Synthesis of supervisors for time-varying discrete event systems

We introduce a time-varying automaton to model discrete event systems. The structure of this time-varying automaton is very similar structure to (max,+) automaton, but allowing variable event lifetimes. Based on this time-varying automaton the design of timed supervisors is obtained by using the dioid algebra, where the languages used to describe the discrete event system as well the desired specification are replaced by matrices defined in such algebra and the supervisor synthesis is achieved through simple matrix operations. The proposed synthesis algorithm allows one to synthesize supervisors for un-timed DES, timed DES with constant event lifetime and timed DES with variable event lifetime. All these cases are treated with the same basic algorithm, the differences rely only on the definition of the event lifetime functions. The proposed algorithm presents a complexity order equal to the supervisor synthesis algorithm of un-timed discrete event systems. The proposed approach can be considered as an alternative procedure, based on a non-traditional algebraic structure, to achieve the supervisor synthesis for discrete event systems.