A Graph Metric for Model Predictive Control of Petri Nets

Abstract

There are many systems that may be described by abstract states like the colors of traffic lights or switch positions. Such systems can be modeled as discrete event systems (DES). Petri nets (PN) are a powerful tool to model DES like production systems, biological systems or communication networks. We present a model predictive control (MPC) approach for Petri net models which is inspired by linear-quadratic regulator (LQR) design. Therefore, we solve the system of diophantine Petri net state equations. Using the solution, we derive a metric for DES which is an analogue to the one associated with the quadratic objective in LQR design. This enables us to relate abstract states to each other and to provide a new distance measure that considers the discontinuous state space of DES. Finally, we present an analogue to the classical MPC formulation known for time-driven systems.