Analysis and control of max-plus linear discrete-event systems
An introduction
B De Schutter (TU Delft - Team Bart De Schutter, TU Delft - Delft Center for Systems and Control)
Ton Van Den Boom (TU Delft - Team Bart De Schutter)
J. Xu (TU Delft - Team Bart De Schutter)
Samira S. Safaei Farahani (TU Delft - Energy and Industry)
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Abstract
The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discrete-event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete-event systems because they can be described by a model that is “linear” in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete-event systems. Next, some control approaches for max-plus linear discrete-event systems, including residuation-based control and model predictive control, are presented briefly. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems.
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