Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
Brief paper: Formulae relating controllability, observability, and co-observability
Automatica (Journal of IFAC)
| Hi-index | 0.98 |
This paper is concerned with building reduced interpreted Petri net (IPN) models of discrete event systems (DES). It introduces two results. The first one is a new modelling methodology and the second one is the definition of transformation matrices used to obtain equivalent IPN. The modelling methodology is based on building binary IPN for the system state variables and deriving a global model using the synchronic and the novel permissive compositions. One advantage of this approach is that the combinatorial tuning phase, used by other methodologies is no longer needed. On the other hand, the transformation matrices are used to obtain reduced IPN versions of the binary IPN obtained with our modelling methodology. The reduced IPN are no longer binary and have a less number of nodes. Since the reachability graph of a reduced IPN is the same that the original net and also the input/output behavior are identical, consequentely all properties of a reduced IPN are the same than the original net; this fact is shown regarding the observability property.