Online Representation-based State Estimation of λ-free Labeled Petri Nets

A new approach for the online state estimation of discrete event systems (DESs) modeled by λ-free labeled Petri nets (λf-LPNs) is presented, wherein all events are observable. Instead of exhaustively enumerating all marking vectors consistent with any given event occurrence, we do a representation-based state estimation, where we compute a compact representation structure that characterizes these markings. Our representation structure is based on a representative Petri net (RPN), whose single initial marking represents all markings of the system λf-LPN consistent with the sequence. These representations can be directly used to solve other DES-related problems, such as fault diagnosis. Our approach can compute representations of any λf-LPNs. In addition, for a class of unbounded λf-LPNs, our approach can compute representations that do not grow indefinitely as more events occur.