Towards a Diagnosability Technique of P-Time Petri Nets Systems

This paper presents a diagnosability technique of a P-time Petri net under partial observation. Indeed, the set of transitions is partitioned into those labeled with the empty string epsilon called silent (as their firing cannot be detected) including the faulty transitions and the observable ones. The diagnosability can be defined as the ability to detect the type of a failure within a finite number of steps after its occurrence - the system is then said to be diagnosable. The proposed approach is based on the synthesis of a modified state observer where the fault transitions are considered as observable allowing the construction of a Sampath-like diagnoser. The novelty of the developed approach resides in the fact that, although the time factor is considered as intervals, the diagnoser is computed thanks to the underlying untimed Petri net structure of the P-time model considered. Furthermore, the method relies on linear programming techniques and the schedulability analysis of particular firing sequences exhibited by the analysis of the obtained diagnoser and does not require the construction of the state class graph.