Abstract
Reconstructing the state of a system from available measurements is a fundamental issue in system theory. It may be considered as a self-standing problem, or it can be seen as a pre-requisite for solving a problem of different nature, such as stabilization, state-feedback control, diagnosis, etc. In the case of Continuous Petri Nets (CPNs), this problem has been studied for both untimed and timed models. In this chapter it is considered first the problem of observability of timed CPNs under infinite server semantics (or variable speed). It is assumed that the marking of some places are measured due to some sensors and the problem is to estimate the initial/ actual state/marking. Three different concepts of observability are defined based on the knowledge of the firing rate vector and, algebraic and graph-based criteria are presented. In the last part, untimed CPNs are considered. Measuring/observing the firing amount in which some transitions are fired, it is shown that the set of possible markings in which the system may be is convex. Based on this characterization, some linear programming problems are presented permitting the computation of diagnosis states when some unobservable transitions model possible faults.
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Mahulea, C., Júlvez, J., Vázquez, C.R., Silva, M. (2013). Continuous Petri Nets: Observability and Diagnosis. In: Seatzu, C., Silva, M., van Schuppen, J. (eds) Control of Discrete-Event Systems. Lecture Notes in Control and Information Sciences, vol 433. Springer, London. https://doi.org/10.1007/978-1-4471-4276-8_19
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DOI: https://doi.org/10.1007/978-1-4471-4276-8_19
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