Modelling and Control for Max-Plus Systems with Partial Synchronization

A max-plus system with partial synchronization is a persistent discrete event system divided into a main subsystem and a secondary subsystem such that the secondary subsystem has to adjust its behavior to the main subsystem, but the main subsystem is not affected by the secondary subsystem. A formal model based on max-plus recursive equations is presented for max-plus systems with partial synchronization. Furthermore, the control problem of output tracking is addressed by assigning a higher priority to the main subsystem: the performance of the main subsystem is never degraded to improve the performance of the secondary subsystem. Two different control approaches are investigated: optimal feedforward control and model predictive control. In both cases, residuation theory is applied to efficiently solve the optimization problem.