Robustness of a Class of Nonordinary Petri Nets

Robustness analysis concerns with the ability for a system to maintain operation in the presence of uncertainties. Existing studies on robustness properties of non-ordinary Petri nets (NPN) are still limited. This motivates us to develop analysis method for NPN. To study the robustness properties of NPN, we first propose a model called non-ordinary controlled Petri net with uncertainties (NCPNU), which specifies an upper bound on the uncertainties for each reachable marking. The computational complexities to characterize the maximal tolerable uncertainties for each reachable marking grow exponentially with the size of the nets. We then limit our scope to a subclass of Petri nets called non-ordinary controlled flexible assembly Petri net with uncertainties (NCFAPNU) and study its robustness. We extend the robustness analysis to NCFAPNU. We identify two types of uncertainties under which the liveness of NCFAPNU can be maintained.