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Independent cycle time assignment for min-max systems

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Abstract

A variety of problems in digital circuits, computer networks, automated manufacturing plants, etc., can be modeled as min-max systems. The cycle time is an important performance metric of such systems. In this paper, we focus on the cycle time assignment of min-max systems which corresponds to the pole assignment problem in traditional linear control systems. For the minmax system with max-plus inputs and outputs, we show that the cycle time can be assigned disjointedly by a state feedback, if and only if the system is reachable. Furthermore, a necessary and sufficient condition for the cycle time to be assigned independently by a state feedback is given. The methods are constructive, and some numerical examples are given to illustrate how the methods work in practice.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, PRC

    Wen-De Chen

  2. Department of Mathematics, Zhengzhou University, Henan, 450001, PRC

    Yue-Gang Tao

  3. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, PRC

    Yue-Gang Tao

  4. Faculty of Computing, Engineering and Technology, Staffordshire University, Stafford, ST16 9DG, UK

    Hong-Nian Yu

Authors
  1. Wen-De Chen
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  2. Yue-Gang Tao
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  3. Hong-Nian Yu
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Corresponding author

Correspondence to Wen-De Chen.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60774007) and the Royal Society of UK.

Wen-De Chen graduated from University of Science and Technology of PRC 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, the Chinese Academy of Sciences, PRC.

His research interests include discrete event systems and coding theory.

Yue-Gang Tao received the Ph.D. degree from the Academy of Mathematics and Systems Science, the Chinese Academy of Sciences, PRC in 2002. He is currently a professor at the Department of Mathematics, Zhengzhou University, PRC, and working at Institute of Automation, the Chinese Academy of Sciences.

His research interest includes algebra, optimization and control, and their applications in discrete-event systems.

Hong-Nian Yu is currently a professor of computer science and the head of the Mobile Computing and Distributed Control Systems Research Group at Staffordshire University, UK. He is the general co-chair IEEE International Conference on Networking, Sensing and Control in 2009, general chair UK EPSRC Postgraduate Workshop on Human Adaptive Mechatronics in 2009, International Program Committee (IPC) co-chair of the United Kingdom Automatic Control Council (UKACC) in 2008, program chair of IEEE Conference on Networking, Sensing and Control in 2007, general chair of International conference on Software Knowledge Information Management and Applications in 2006, and is serving on various other conferences and academic societies.

His research interests include experience in neural networks, mobile computing, modelling, control of robot manipulators, and modelling, scheduling, planning, and simulations of large discrete event dynamic systems with applications to manufacturing systems, supply chains, transportation networks, and computer networks.

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Chen, WD., Tao, YG. & Yu, HN. Independent cycle time assignment for min-max systems. Int. J. Autom. Comput. 7, 254–260 (2010). https://doi.org/10.1007/s11633-010-0254-9

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  • DOI: https://doi.org/10.1007/s11633-010-0254-9

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