Robustness analysis of non-ordinary Petri nets for flexible assembly systems

Abstract

Non-ordinary controlled Petri nets (NCPNs) have the advantages to model flexible assembly systems in which multiple identical resources may be required to perform an operation. However, existing studies on NCPNs are still limited. For example, the robustness properties of NCPNs have not been studied. This motivates us to develop an analysis method for NCPNs. Robustness analysis concerns the ability for a system to maintain operation in the presence of uncertainties. It provides an alternative way to analyse a perturbed system without reanalysis. In our previous research, we have analysed the robustness properties of several subclasses of ordinary controlled Petri nets. To study the robustness properties of NCPNs, we augment NCPNs with an uncertainty model, which specifies an upper bound on the uncertainties for each reachable marking. The resulting PN models are called non-ordinary controlled Petri nets with uncertainties (NCPNU). Based on NCPNU, the problem is to characterise the maximal tolerable uncertainties for each reachable marking. The computational complexities to characterise maximal tolerable uncertainties for each reachable marking grow exponentially with the size of the nets. Instead of considering general NCPNU, we limit our scope to a subclass of PN models called non-ordinary controlled flexible assembly Petri net with uncertainties (NCFAPNU) for assembly systems and study its robustness. We will extend the robustness analysis to NCFAPNU. We identify two types of uncertainties under which the liveness of NCFAPNU can be maintained.