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

Control procedure and stability conditions

Master thesis (2022)

Authors

J.C.M. Kroese Mechanical Engineering

Contributors

A.J.J. van den Boom Team Ton van den Boom - Mechanical, Maritime and Materials Engineering (supervisor 1)
M. Jafarian Team Matin Jafarian - Mechanical, Maritime and Materials Engineering (supervisor 2)
Faculty
Mechanical Engineering
Copyright: © 2022 Justine Kroese
MPC Discrete-event systems MMPS
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Published Date

17-11-2022

Language

English

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Faculty

Mechanical Engineering

Abstract

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.