Cagliari, Italy
In this talk I discuss the problem of estimating the marking of a Place/Transition net based on event observation, assuming that the net structure is known while the initial marking is totally or partially unknown.
It is possible to compute a marking estimate that is always a lower bound of the actual marking, and the special structure of Petri nets allows one to use a simple linear algebraic formalism for estimate and error computation.
The error between actual marking and estimate is a monotonically non-increasing function of the observed word length, and words that lead to null error are said complete. It is possible to define several observability properties related to the existence of complete words. To prove some of them there exists a useful tool, the observer coverability graph, i.e., the usual coverability graph of a Place/Transition net augmented with a vector that keeps track of the estimation error on each place of the net.
Finally, I will show how the estimate generated by the observer may be used to design a state feedback controller for forbidden marking specifications.