NDLI: 3D visualization of region of stabilization for nonlinear systems using FPGA

Content Provider	IEEE Xplore Digital Library
Author	Funasaka, T. Iwase, M. Hatakeyama, S.
Copyright Year	2004
Description	Author affiliation: Graduate Sch. of Sci. & Eng., Tokyo Denki Univ., Saitama, Japan (Funasaka, T.; Iwase, M.; Hatakeyama, S.)
Abstract	The stabilization of nonlinear systems depends strongly on the initial state and the parameters of the systems. The initial state and the parameters with which the system is stabilized can be distinguished by the geometrical structure. It is, however, difficult and sometimes impossible to analyze the structure analytically. Therefore it comes important to show and analyze the structure of the parameters and initial states numerically and visually. In this paper, we present a method to draw and visualize such region and structure in the three dimensional space. In general, the projection of the original high-dimensional space to the lower dimension one is required for using visual analysis. Thus, it is convenient that the viewpoint can be moved, without time loss, in the direction where analyst would like to see. As often as the viewpoint moves, the recomputation as quick as possible is required to realize the quick motion of viewpoint. It is, however, obvious that lots of computation and time are taken to draw the region. Therefore, high performance calculators are needed to realize the real-time drawing. In order to overcome this problem, FPGA is used in this paper. Then it is demonstrated by illustrative examples that FPGA shows high performance lo draw the region of the parameters and initial state in 3D with which Z/sub n+1/=Z/sub n//sup 2/+C can be stabilized, that is Mandelbrot and Julia sets, respectively.
Starting Page	2154
Ending Page	2158
File Size	871393
Page Count	5
File Format	PDF
ISBN	0780387309
DOI	10.1109/IECON.2004.1432130
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-11-02
Publisher Place	South Korea
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Visualization Nonlinear systems Field programmable gate arrays Stability analysis Calculators Nonlinear control systems Control systems Circuits Fractals Programmable logic arrays
Content Type	Text
Resource Type	Article

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