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力学进展 ›› 2017, Vol. 47 ›› Issue (1): 201705-201705.doi: 10.6052/1000-0992-16-027

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Cell mapping methods-beyond global analysis of nonlinear dynamic systems(非线性动力学系统全局分析之外的胞映射方法新发展)

孙建桥1, 熊夫睿2   

  1. 1 加州大学默塞德分校工学院, 美国加利福尼亚州 95343;
    2 中国核动力研究设计院, 成都 610041
  • 收稿日期:2016-08-23 修回日期:2016-10-10 出版日期:2017-01-01 发布日期:2016-10-10
  • 通讯作者: Jian-Qiao SUN, Dr.Jian-Oiao Sun obtained his Ph.D.in Mechanical Engineering from University of California at Berkeley in 1988. E-mail:jqsun@ucmerced.edu

Cell mapping methods-beyond global analysis of nonlinear dynamic systems

JianQiao SUN1, FuRui XIONG2   

  1. 1 School of Engineering, University of California, Merced, CA 95343, USA;
    2 Nuclear Power Institute of China, Chengdu 610041, China
  • Received:2016-08-23 Revised:2016-10-10 Online:2017-01-01 Published:2016-10-10
  • Contact: 10.6052/1000-0992-16-027 E-mail:jqsun@ucmerced.edu
  • Supported by:

    The material in this paper is based on work supported by grants (11172197, 11332008, and 11572215) from the National Natural Science Foundation of China, and a grant from the University of California Institute for Mexico and the United States (UC MEXUS) and the Consejo Nacional de Cienciay Tecnología de México (CONACYT) through the project "Hybridizing Set Oriented Methods and Evolutionary Strategies to Obtain Fast and Reliable Multi-objective Optimization Algorithms".

摘要:

在20世纪80年代由徐皆苏教授创建的胞映射方法一直受非线性科学界同仁的欢迎.近几年胞映射方法有了许多新的应用和算法.本文介绍了一些控制应用和算法的文献.另外,还介绍和讨论胞映射方法应用与多目标优化问题的研究和方法,多目标优化控制设计和非线性代数方程找零解.文中指出胞映射方法在并行计算的帮助下,现在可以解决中等高维空间中的各类问题,新的应用还会不断出现.

关键词:

胞映射方法|全局分析|最优控制|多目标优化|非线性代数方程的零解

Abstract:

The cell mapping methods created by Hsu in 1980s have been popular choices for the researchers in nonlinear science communities. There have been new applications and new algorithm developments of the cell mapping methods. This paper presents a discussion of the literature of some control applications and recent algorithm developments of the cell mapping methods. In particular, we present studies of multi-objective optimization problems with the cell mapping methods, multi-objective optimal control designs, and zeros finding of nonlinear algebraic equations. The problems solved with the cell mapping methods are now in moderately high dimensional space with the help of parallel computing.

Key words:

cell mapping methods|global analysis|optimal control|multi-objective optimization|finding zeros

中图分类号: 

  • O322