On the Properties of the Greatest Subsolution for Linear Equations in the Max-Plus Algebra(Systems and Control)

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概要

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• This paper examines the properties of the greatest subsolution for linear equations in the max-plus algebra. The greatest subsolution is a relaxed solution of the linear equations, and gives a unified and reasonable solution whether there exists a strict solution or not. Accordingly, it forms part of a key algorithm for deriving a control law in the field of controller design, and some effective controllers based on the greatest subsolution have been proposed. However, there remain several issues to be discussed regarding the properties of the greatest subsolution. Hence, the main focus of this paper is on the following fundamental properties: 1) Formulation as an optimization problem, 2) Uniqueness of the greatest subsolution, 3) Necessary and sufficient condition for the correspondence of the greatest subsolution with the strict solution. These results could provide flexibility of the controller design based on the greatest subsolution, and facilitate the performance evaluation of the controller. Finally, the uniqueness of the strict solution of the linear equations is examined, and it is confirmed through illustrative examples.

• 社団法人電子情報通信学会の論文
• 2004-02-01

著者

• MASUDA Shiro

  Tokyo Metropolitan University

• Masuda Shiro

  Tokyo Metropolitan Institute Of Technology

• Goto Hiroyuki

  Japan Research Institiute Ltd.

関連論文

• Consideration of Capacity and Order Constraints for Event-Varying MPL Systems(Systems and Control)
• On the Properties of the Greatest Subsolution for Linear Equations in the Max-Plus Algebra(Systems and Control)
• Modeling for Systems with Selective Parameters Based on the Max-Plus Linear Algebra(Systems and Control)

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