Petri net state estimators based on event observation

We discuss the problem of estimating the marking of a place/transition net based on event observation. We assume that the net structure is known while the initial marking is totally or partially unknown. We give two algorithms to compute a marking estimate that is a lower bound of the actual marking. The error between actual marking and estimate is a monotonically nonincreasing function of the observed word length. The special structure of Petri nets allows us to use a simple linear algebraic formalism for estimate and error computation. In particular, the set of markings consistent with an observed word, i.e., the set of marking in which the system may actually be given the observed word, can be easily characterized. Finally, we show how the estimate generated by the observer may be used to design a state feedback controller