Abstraction of Hybrid Systems

Abstract

Disturbances are an important factor in the performance of complex large scale systems. These complex large scale systems can be modeled by a broad class of hybrid dynamical systems. The current practice of controlling such processes is one way, from the scheduling level to the control level. The performance of these complex systems can be improved by allowing an exchange of information between both the scheduling and control level.

Although the techniques derived in this thesis are applicable to general class of hybrid systems, this thesis focuses on a railway network. This network, or a part of it, is modeled so that information at regular time instances can be sent to a dynamic scheduler which outputs an optimal schedule back to the control level, based on the current conditions in the network.

To this end, the railway system is abstracted into a Discrete-event system (DES). Essentially, the abstraction removes the continuous dynamics of a hybrid dynamical model and replaces them with discrete-events. All these discrete-events together form the railway network as a DES. Furthermore, the DES is modeled in max-plus algebra such that a Max-plus linear (MPL) is obtained.

The scheduling problem is solved by a Model predictive control (MPC) scheme which is solved by a Mixed-integer linear programming (MILP) problem. For this scheme, the MPL model is converted into a Switching max-plus linear (SMPL) model which is written as a set of mixed-integer linear constraints. In contrast to the scheduler which only contains a macroscopic model of the railway network, the trajectory planner includes microscopic constraints. Therefore, to complete the scheduling, the schedule found by the scheduler is iterated between the scheduler and a trajectory planner for further improvements. A part of a railway network is studied in a case study, showing that updating the schedule results in less delay in case a delay is introduced.