Observability of continuous Petri nets with infinite server semantics

Timed continuous Petri net (contPN) systems with infinite server semantics are non-linear systems, particularly a subclass of piecewise linear (PWL) systems. This paper addresses several problems regarding the state observability of these systems. We assume that the initial marking/state is not known and measuring the marking of some places we want to estimate all the others. First, a study of the different linear systems corresponding to a continuous Petri net system is performed. It is shown that in some cases, some of them are redundant, and so can be disregarded. The notion of distinguishable modes is introduced helping to give a necessary and sufficient criterion for the observability in infinitesimal time. Structural observability, i.e., observability for all possible values of firing rates of transitions, is studied and it is proved that in some cases it can be reduced to a linear problem, even if the system is nonlinear. Using results from linear structured systems, the concept of weak structural or generic observability is considered. To be published as: C. Mahulea, L. Recalde, and M. Silva, ”Observability of continuous Petri nets with infinite server semantics”, Nonlinear Analysis: Hybrid Systems, 2009, doi:10.1016/j.nahs.2009.06.014. Corresponding author C. Mahulea. Tel. +34-976-762517. Fax +34-976761914. This work was partially supported by the CICYT FEDER project DPI200615390. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no 224498. ∗The authors are with are with the Department of Computer Science and System Engineering, University of Zaragoza, Maria de Luna 1, 50018 Zaragoza, Spain {cmahulea, [email protected]}.