B. De Schutter and T. van den Boom, "Model predictive control for discrete-event systems with soft and hard synchronization constraints," Proceedings of the Workshop on Max-Plus Algebras and Their Applications to Discrete-Event Systems, Theoretical Computer Science, and Optimization, Prague, Czech Republic, 6 pp., Aug. 2001.
Max-plus-linear models can be used to model discrete-event systems with only synchronization and no concurrency. The synchronization constraints in max-plus-linear discrete-event systems are hard, i.e., they cannot be broken under any circumstance. We consider a class of discrete-event systems with both hard and soft synchronization constraints, i.e., if necessary, some synchronization conditions may be broken, but then a penalty is incurred. We show that - after introducing control variables - this leads to a max-plus-bilinear model. Furthermore, we also show how the model predictive control (MPC) framework can be extended to this class of discrete-event systems.