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Balance properties and stabilization of min-max systems

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Abstract

A variety of problems in operations research, performance analysis, manufacturing, and communication networks, etc., can be modelled as discrete event systems with minimum and maximum constraints. When such systems require only maximum constraints (or dually, only minimum constraints), they can be studied using linear methods based on max-plus algebra. Systems with mixed constraints are called min-max systems in which min, max and addition operations appear simultaneously. A significant amount of work on such systems can be seen in literature. In this paper we provide some new results with regard to the balance problem of min-max functions; these are the structure properties of min-max systems. We use these results in the structural stabilization. Our main results are two sufficient conditions for the balance and one sufficient condition for the structural stabilization. The block technique is used to analyse the structure of the systems. The proposed methods, based on directed graph and max-plus algebra are constructive in nature. We provide several examples to demonstrate how the methods work in practice.

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Authors and Affiliations

  1. Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing, 100080, PRC

    Yue-Gang Tao

  2. Laboratory of Systems and Control, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, PRC

    Wen-De Chen

  3. School of Information Engineering, University of Science and Technology Beijing, Beijing, 100083, PRC

    Yi-Xin Yin

Authors
  1. Yue-Gang Tao
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  2. Wen-De Chen
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  3. Yi-Xin Yin
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Corresponding author

Correspondence to Yue-Gang Tao.

Additional information

This work was supported by National Natural Science of China (No.69874040), the National Key Project of China, and the Hundred Talents Program of the Chinese Academy of Sciences.

Wende Chen graduated from University of Science and Technology of China in 1964.

He is a full Professor of the Institute of Systems Science, which is now a part of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include mainly in discrete event systems and coding theory. He has over 100 publications on these fields.

Yixin Yin received the B.S., M.S. and Ph.D degrees from University of Science and Technology Beijing (USTB), China, in 1982, 1984 and 2002, respectively.

He is currently a professor and Dean of School of Information Engineering in the School of Information Engineering of USTB. His main research interests include intelligent control, adaptive control and Artificial Life (AL). He has published over 50 papers on these fields.

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Tao, YG., Chen, WD. & Yin, YX. Balance properties and stabilization of min-max systems. Int J Automat Comput 3, 76–83 (2006). https://doi.org/10.1007/s11633-006-0076-y

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  • DOI: https://doi.org/10.1007/s11633-006-0076-y

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