State estimation of max-plus automata with unobservable events

The state estimation problem is a fundamental issue in discrete event systems. Partial observations arise when the occurrence of some events cannot be detected. The considered problem then consists in finding all the states in which the system may be when an observed sequence is given. To the best of our knowledge there are few works dealing with this problem in the framework of timed discrete event systems. In this paper we investigate state estimation for systems represented as max-plus automata. Max-plus automata represent a particular class of weighted automata and if a timed interpretation is given to weights, then max-plus automata are strongly related to timed automata. We first give the definition of consistent states with respect to an observed timed sequence and a given time instant. Then, based on the state vectors of a max-plus automaton, an algorithm is proposed to compute the set of all consistent states