B. De Schutter and T.J.J. van den Boom, "Model predictive control for max-min-plus-scaling systems - Efficient implementation," Proceedings of the 6th International Workshop on Discrete Event Systems (WODES'02) (M. Silva, A. Giua, and J.M. Colom, eds.), Zaragoza, Spain, pp. 343-348, Oct. 2002.
In previous work we have introduced model predictive control (MPC) for max-plus-linear and max-min-plus(-scaling) discrete-event systems. For max-plus-linear systems there are efficient algorithms to solve the corresponding MPC optimization problems. However, previously, for max-min-plus(-scaling) systems the only approach was to consider a limited subclass of decoupled max-min-plus systems or to use nonlinear nonconvex optimization algorithms, which are not efficient if the size of the system or the MPC optimization problem is large. In this paper, we present a more efficient approach that is based on canonical forms for max-min-plus-scaling functions and in which the MPC optimization problem is reduced to a set of linear programming problems.