The interaction between scheduling and control of semi-cyclic hybrid systems

In this paper a new iterative approach is proposed for the design of a combined real-time scheduling and control algorithm that can be applied to industrial systems that are described by a hybrid model with a (semi-)cyclic behavior. Traditionally scheduling and control problems are considered in a sequential way. First the scheduling problem is solved and subsequently the control problem. This may result in inconsistent solutions such that the system may not operate adequately and does not reach the desired operational targets. In our approach scheduling is done with model predictive control using a switching max-plus linear model of the discrete event part of the system. The interface with a reference generator determines whether the computed reference signal will lead to a feasible response. Furthermore, it estimates the duration of the operations in the system based on the actual state, and communicates that with the scheduler. In an iterative procedure the optimal and feasible schedule can be computed. In a case study the railway traffic on a single track is considered, showing that updating the schedule results in feasible local speed profiles for the trains and less delay in the overall system in case of a delay.