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Independent Cycle Time Assignment for min-max systems

International Journal of Automation and computing 2010年第2期7卷 254-260页

作者： Wen-De Chen Yue-Gang Tao Hong-Nian Yu Academy of Mathematics and systems Science Chinese Academy of Sciences Beijing 100190 PRC Department of Mathematics Zhengzhou University Henan 450001 PRC Institute of Automation Chinese Academy of Sciences Beijing 100190 PRC Faculty of Computing Engineering and Technology Staffordshire University Stafford ST16 9DG UK

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 minimax systems which corresponds to the pole assignment problem in traditional linear control systems. For the min- max 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.

关键词： Cycle time coloring graph independent assignment min-max systems state feedback.

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Balance Properties and Stabilization of min-max systems

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International Journal of Automation and computing 2006年第1期3卷 76-83页

作者： Yue-Gang Tao Wen-De Chen Yi-Xin Yin Laboratory of Complex systems and Intelligence Science Institute of Automation Chinese Academy of Sciences Beijing 100080 PRC Laboratory of systems and Control Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 PRC School of Information Engineering University of Science and Technology Beijing Beijing 100083 PRC

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 rain, 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.

关键词： Balance fixed point min-max systems output feedback structural stabilization.

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Inseparability of min-max systems

Inseparability of Min-Max Systems

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第二十二届中国控制会议

作者： Zhao Qianchuan Department of Automation, Tsinghua University, Beijing 100084

＜正＞min-max systems, or min-max-plus systems are algebraic models of Discrete Event Dynamic systems. They are non-linear extension of the well known linear max-plus system models. In this paper, we survey our recent research results related to the structural property "inseparability" of min-max systems proposed in [24]. It turns out inseparability has very interesting relationship to many aspects of min-max systems. It has been applied to the stabilization of min-max systems. It also has interesting implications to other important research areas including bio-informatics and artificial neural networks.

关键词： min-max systems Eigen-structure Inseparability Structural property.

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