On-line diagnosis for time Petri nets

We derive in this paper on-line algorithms for fault diagnosis of Time Petri Net (TPN) models. The plant observation is given by a subset of transitions while the faults are represented by unobservable transitions. The model-based diagnosis uses the TPN model to derive the legal traces that obey the received observation and then checks whether or not fault events occurred. To avoid the consideration of all the interleavings of the concurrent transitions, the plant analysis is based on partial orders (unfoldings). The legal plant behavior is obtained as a set of configurations. The set of legal traces in the TPN is obtained solving a system of (max,+)linear inequalities called the characteristic system of a configuration. We present two methods to derive the entire set of solutions of a characteristic system, one based on Extended Linear Complementarity Problem and the second one based on constraint propagation that exploits the partial order relation between the events in the configuration.