A new class of Petri nets for modeling and control of ratio-enforced resource allocation systems

This paper presents a class of Petri nets that can well model ratio-enforced resource allocation systems (RASs). Such RASs are required to enforce certain ratio among their processes to meet a desired production plan. A ratio-enforced system of sequential systems with shared resources (RS⁴R) can model an RAS whose processes are described by state machines. Both a ratio-enforcing controller and liveness-enforcing supervisor must be designed to fulfil the deadlock-free and ratio-constrained production of products. We theoretically prove that their design can be separately performed.