B. De Schutter and T.J.J. van den Boom, "MPC for discrete-event systems with soft and hard synchronisation constraints," International Journal of Control, vol. 76, no. 1, pp. 82-94, Jan. 2003.
Discrete-event systems with only synchronisation and no concurrency, also known as timed event graphs or (max,+)-linear systems, have been studied by several authors. The synchronisation constraints that arise in these discrete-event systems are hard, i.e., they cannot be broken under any circumstance. In this paper we consider a more extended class of discrete-event systems with both hard and soft synchronisation constraints, i.e., if necessary, some synchronisation conditions may be broken, but then a penalty is incurred. We show how the model predictive control (MPC) framework, which is a very popular controller design method in the process industry, can be extended to this class of discrete-event systems. In general, the MPC control design problem for discrete-event systems with soft and hard synchronisation constraints leads to a nonlinear non-convex optimisation problem. We show that the optimal MPC strategy can also be computed using an extended linear complementarity problem.