Model Predictive Control on Max-min-plus-scaling Systems

Model Predictive Control on Max-min-plus-scaling Systems: Control procedure and stability conditions

Kroese, Justine (TU Delft Mechanical, Maritime and Materials Engineering)

van den Boom, A.J.J. (mentor)
Jafarian, M. (graduation committee)

Delft University of Technology

Mechanical Engineering | Systems and Control

2022-11-17

Max-plus-linear (MPL) systems are systems that are linear in max-plus algebra. A generalization of these systems are Max-Min-Plus-Scaling (MMPS) systems. Next to maximization and addition (plus), MMPS systems use the operations minimization and scaling. They are discrete-event (DE) systems, which means that the changing of the states is triggered by the occurrence of events and (part of) the states in the state vector represent time instances. One way to control MMPS systems is by using Model predictive control (MPC). This is a powerful
on-line control strategy that uses a receding horizon. However, an efficient control procedure that works for all time-invariant DE MMPS systems had not yet been described. The goal of this master thesis is to fully design such a framework. To achieve this, the state vector is altered, such that the difference in the states that represent a time instance is included as well. Next to this, the MPC problem on an MMPS system is altered to a Mixed integer quadratic programming (MIQP) problem, in order to optimize it more efficiently. That this framework
works is supported by a stability analysis. Next to that, it is tested on a simulation example of an urban railway line. Based on this example, it is shown that the procedure does indeed work. The thesis ends with several suggestions for future research.

MPC
MMPS
Discrete-event systems

http://resolver.tudelft.nl/uuid:7d55d679-0beb-40f6-bf07-793b64895032

Student theses

master thesis

© 2022 Justine Kroese