Properties of continuous Petri nets controlled via model predictive control

Abstract

In previous papers we investigated the problem of deriving an optimal control law for continuous Petri nets under infinite server semantics. In particular, the problem was studied through Model Predictive Control (MPC), an advanced control method, extensively used in industrial applications. In this work we discuss some properties of the resulting closed-loop system, such as feasibility and asymptotic stability. We prove that for continuous Petri nets feasibility is always guaranteed, while asymptotic stability is not ensured. Finally, we demonstrate that the introduction of an appropriate terminal constraint may guarantee asymptotic stability provided that certain assumptions on the initial state and the moving horizon are satisfied.