Performance control of Markovian Petri nets via fluid models: A stock-level control example

Petri nets is a well-know formalism for studying discrete event systems. Applications include performance evaluation in communication networks, production systems, supply chains, and the implementation of sequence controllers. Timed Continuous Petri Net (TCPN) systems are continuous-state models that can approximate the dynamical behavior of discrete Markovian Petri nets (MPN). Based on this, an estimator-based control structure is introduced here for applying a control law designed for a TCPN into the original discrete system. The result is a control policy for driving a MPN system in such a way that the mean value of its marking will reach a desired value, by applying additional delays to the controllable transitions. A stock level control of a Kanban-based automotive assembly line is synthesized as an application example.