G. Jiroveanu, B. De Schutter, and R.K. Boel, "The on-line diagnosis of time Petri nets based on partial orders," Chapter 21 in Taming Heterogeneity and Complexity of Embedded Control (F. Lamnabhi-Lagarrigue, S. Laghrouche, A. Loria, and E. Panteley, eds.), London, UK: ISTE, ISBN 978-1-905209-65-1, pp. 363-391, Jan. 2007.
In this paper we propose an on-line diagnosis algorithm for Time Petri Nets (TPN). The plant observation is given by a subset of transitions and the faults are modeled by a subset of unobservable transitions. The plant behavior is derived on-line and the diagnosis is obtained checking whether or not some or all of the traces in the behavior that obey the plant observation contain fault events. We calculate the legal plant behavior as a set of configurations in the net unfolding. We calculate the set of legal traces in the TPN deriving for each configuration the solution set of a system of (max,+)-linear inequalities called the characteristic system of the configuration. We present two methods to derive the entire set of solutions of a characteristic system: the first method is based on Extended Linear Complementarity Problem while the second method is based on constraint propagation.