Stability analysis using higher order derivatives of universal learning networks

Yunqing Yu, Kotaro Hirasawa, Takayuki Furuzuki, Junichi Murata

研究成果: Article

抄録

Stability is one of the most important subjects in the control performance. As for the stability analysis of nonlinear systems in the past, Lyapunov method and linear stability methods based on linear approximation of nonlinear systems have been used. But, in many cases when Lyapunov method is applied, it is difficult to find suitable Lyapunov functions. And when using linear approximation, it can not be decided whether nonlinear systems are stable or not on the outside of the region where linear stability theory can be applied. Therefore, a new stability analysis method is required to develop, which can be easily applied to nonlinear systems. In this paper, stability analysis based on the higher order derivatives of Universal Learning Networks (ULNs) and its application to nonlinear systems are discussed. The stability analysis using ULNs is studied by the deviation of the system dynamics. The deviation of the system dynamics can be calculated by the higher order derivatives of ULNs. In this paper, simulations of an inverted pendulum balancing system are carried out. From the results of the simulations, it is shown that the inverted pendulum can be controlled effectively by ULNs. In addition, it is clarified that the stability of the nonlinear systems is easily analyzed by using the stability analysis of ULNs.

元の言語English
ページ(範囲)193-207
ページ数15
ジャーナルResearch Reports on Information Science and Electrical Engineering of Kyushu University
5
発行部数2
出版物ステータスPublished - 2000 9
外部発表Yes

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Derivatives
Nonlinear systems
Lyapunov methods
Pendulums
Dynamical systems
Lyapunov functions

ASJC Scopus subject areas

  • Hardware and Architecture
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering

これを引用

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title = "Stability analysis using higher order derivatives of universal learning networks",
abstract = "Stability is one of the most important subjects in the control performance. As for the stability analysis of nonlinear systems in the past, Lyapunov method and linear stability methods based on linear approximation of nonlinear systems have been used. But, in many cases when Lyapunov method is applied, it is difficult to find suitable Lyapunov functions. And when using linear approximation, it can not be decided whether nonlinear systems are stable or not on the outside of the region where linear stability theory can be applied. Therefore, a new stability analysis method is required to develop, which can be easily applied to nonlinear systems. In this paper, stability analysis based on the higher order derivatives of Universal Learning Networks (ULNs) and its application to nonlinear systems are discussed. The stability analysis using ULNs is studied by the deviation of the system dynamics. The deviation of the system dynamics can be calculated by the higher order derivatives of ULNs. In this paper, simulations of an inverted pendulum balancing system are carried out. From the results of the simulations, it is shown that the inverted pendulum can be controlled effectively by ULNs. In addition, it is clarified that the stability of the nonlinear systems is easily analyzed by using the stability analysis of ULNs.",
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AU - Hirasawa, Kotaro

AU - Furuzuki, Takayuki

AU - Murata, Junichi

PY - 2000/9

Y1 - 2000/9

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