Sensor Placement for Distinguishability in Continuous Timed Petri Nets

Abstract

This work is concerned with the sensor placement problem for distinguishability in continuous timed Petri nets with infinite servers semantics (ContPN). The ContPN are considered to be composed by a family of linear systems (LS) switching among them. Depending on the ContPN marking, a LS is chosen to evolve. Thus the distinguishability problem deals with the possibility of determining which LS is evolving, and the sensor placement for distinguishability problem deals with selecting which places must be measured to ensure distinguishability. This work presents two main contributions. The first one shows that there exist cases where the classical theorems in switched linear systems cannot be used in ContPN, since these theorems could establish that the ContPN is not distinguishable, even when, using the ContPN structure, the distinguishability is guaranteed. The second contribution is an algorithm devoted to place sensors (to build the output map) in such a way that the ContPN becomes distinguishable. The input to the algorithm is the output map S, computed as in a previous work, which guarantees that every LS of the ContPNis observable. Then new sensors are included to gain distinguishability between ever pair of LS. Thus the distinguishability and observability of the ContPN is guaranteed.