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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.
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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. -
Figure 1.Two-dimensional projections of a six-dimensional strange attractor of the Lorenz system. Blue dots are the centers of the cells in the invariant set. Red dots showing the fine structure of the attractor are generated with interpolation
Figure 2.The 5-dimensional Pareto front of the objective functions, projected on to 2-dimensional sub-spaces of the objective space. The color code indicates the level ofMp,x1,IAEx2, max |x2|, andtp,x1in subplots from upper left in counterclockwise order. The conflicting nature among these objectives can be observed clearly. For example, the overshoot and peak time are conflicting for tracking control, which can be seen in the upper left plot ofx1
Figure 3.Experimental square wave tracking response of the rotary flexible joint under a Pareto optimal sliding mode control.x1is the base angle andx2is the angle of the flexible link
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