State Estimation of Timed Labeled Petri Nets With Unobservable Transitions

The aim of this paper is to reconstruct the least/greatest sequence of unobservable transitions in timed Petri nets based on the online observation of firing occurrences of some transitions on a sliding horizon. The Petri net, which can be unbounded and can contain self-loops and circuits, is described under an algebraic form composed of A.x <= b which expresses the possible time sequence x and the fundamental marking relation. Under the assumption of Backward/Forward Conflict Freeness of the unobservable-induced subnet, we show the existence of a finite least/greatest sequence with respect to the data known on a given horizon. A technique of computation using linear programming is given. Note to Practitioners-In many processes, it is not always possible to associate a sensor with each state due to the cost and the physical location. In most control applications, not all state variables are measurable. This characteristic can be found in many discrete-event systems such as manufacturing systems, microcircuit design, transportation systems, and the food industry. The variables in discrete-event systems express events such as the beginning/end of a task, the departure/arrival of a train at a railroad crossing, etc. However, the unknown data can be crucial for the control system which supervises the process. In particular, the knowledge of the timestamps of these past events allows future actions to be determined. The technique proposed in this paper is based on a specific calculation of the unknown numbers of events by using the known data on a sliding horizon.