Sensor placement for distinguishability and single structure observer design in continuous timed Petri nets

This work is concerned with the sensor placement problem for distinguishability and the observer design in continuous timed Petri nets with infinite servers semantics (ContPN). The ContPN  are represented by a family of linear systems (LS) switching among them. Depending on the ContPN  marking, a LS evolves. Thus the distinguishability problem deals with the possibility of determining which LS is actually evolving, and the sensor placement for distinguishability problem deals with selecting which places must be measured to ensure distinguishability. On the other hand, the observer’s design problem is concerned with developing a mathematical entity devoted to compute the actual state of the ContPN  by means of the knowledge of the marking in the places which have a sensor.This work presents three 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 an output map SS, that can be computed as in a previous work, which guarantees that every LS of the ContPN  representation is observable. Then new sensors are included to gain distinguishability between every pair of LS. Thus the distinguishability and observability of the ContPN  is guaranteed. Finally, the third main contribution is a single structure observer for the bounded and observable ContPN. This strategy is relevant to avoid the need of computing one observer per LS in the family that represents the ContPN, which in practice becomes unfeasible.