Fault Diagnosis of Discrete-Event Systems using Continuous Petri Nets -draft-

When discrete event systems are used to model systems with a large number of possible (reachable) states, many problems such as simulation, optimization, and control, may become computationally prohibitive because they require some enumeration of such states. A common way to effectively address this issue is fluidization. The goal of this paper is that of studying the effect of fluidization on fault diagnosis. In particular, we focus on the purely logic Petri net model that results in the untimed continuous Petri net model after fluidization. In accordance to most of the literature on discrete event systems, we define three diagnosis states, namely N , U and F , corresponding respectively to no fault, uncertain and fault state. We prove that, given an observation, the resulting diagnosis state can be computed solving linear programming problems rather than integer programming problems as in the discrete case. The main advantage of fluidization is that it enables to deal with much more general Petri net structures. In particular, the unobservable subnet needs not be acyclic as in the discrete case. Moreover, the compact representation of the set of consistent markings using convex polytopes can be seen in some cases as an improvement in terms of computational complexity. Published as: C. Mahulea, C. Seatzu, M.P. Cabasino, and M. Silva, “Fault Diagnosis of Discrete-Event Systems using Continuous Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 42, no. 4, pp. 970 984, July 2012.. DOI: 10.1109/TSMCA.2012.2183358 C. Mahulea and M. Silva are with the Aragón Institute of Engineering Research (I3A), University of Zaragoza, Maria de Luna 1, 50018 Zaragoza, Spain {cmahulea, [email protected]}. M.P. Cabasino and C. Seatzu are with the Department of Electrical and Electronic Engineering, University of Cagliari, Piazza D’Armi, 09123 Cagliari, Italy {cabasino,[email protected]}. This work has been partially supported by the European Community’s Seventh Framework Programme under project DISC (Grant Agreement n. INFSO-ICT-224498). At University of Zaragoza the work has been partially supported also by CICYT FEDER project DPI201020413 and by Fundación Aragón I+D. This paper is based on our results in [1–3].