Observer Construction for Polynomially Ambiguous Max-Plus Automata

In this article, we deal with state estimation of timed discrete event systems that are modeled by max-plus automata (MPAs), where only some events are observable. For a given MPA, a formal procedure is first proposed for constructing its observer by extending our previous concept of observer for unambiguous MPAs to polynomially ambiguous MPAs. As an application, we present a necessary and sufficient condition based on the constructed observer to check the critical observability of MPAs. The state set of an MPA is divided into two disjoint subsets, i.e., the set of critical states and the set of noncritical states. A system is critically observable if the set of all states that are consistent with any observation is either a subset of the critical states set or a subset of the noncritical states set.