Recently, the model predictive control (MPC) framework was applied to a class of discrete event systems, namely max-plus-linear (MPL) systems. The results obtained so far cannot guarantee a priori stability for the MPC and moreover, only input constraints are considered. In this talk we give first a short introduction to MPL systems. Next, we highlight the analogies and differences between stability for conventional MPC and MPC for MPL systems. A priori stabilization conditions for the MPC based on terminal cost, terminal state constraints are derived. We show that the computation of an invariant set can be done in a finite number of steps. Using the cost function, we can prove ``stability in the sense of Lyapunov'' for the MPC scheme. We also discuss under which conditions the optimization problems that arise in MPL-MPC can be solved efficiently.
Possible applications for the new MPC approach include: manufacturing systems, scheduling of railway networks, and optimal traffic signal control.
Back to Control Seminars Page