• Title/Summary/Keyword: Universal approximation theorem

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Robust adaptive fuzzy controller for an inverted pendulum

  • Seo, Sam-Jun;Kim, Dong-Sik
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.1267-1271
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    • 2003
  • This paper proposes an indirect adaptive fuzzy controller for general SISO nonlinear systems. No a priori information on bounding constants of uncertainties including reconstruction errors and optimal fuzzy parameters is needed. The control law and the update laws for fuzzy rule structure and estimates of fuzzy parameters and bounding constants are determined so that the Lyapunov stability of the whole closed loop system is guaranteed. The computer simulation results for an inverted pendulum system show the performance of the proposed robust adaptive fuzzy controller.

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Approximation of the functional by neural network and its application to dynamic systems (신경회로망을 이용한 함수의 근사와 동적 시스템에의 응용)

  • 엄태덕;홍선기;김성우;이주장
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.313-318
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    • 1994
  • It is well known that the neural network can be used as an universal approximater for functions and functionals. But these theoretical results are just an existence theorem and do not lead to decide the suitable network structure. This doubfulness whether a certain network can approximate a given function or not, brings about serious stability problems when it is used to identify a system. To overcome the stability problem, We suggest successive identification and control scheme with supervisory controller which always assures the identification process within a basin of attraction of one stable equilibrium point regardless of fittness of the network.

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Adaptive Nonlinear Control of Helicopter Using Neural Networks (신경회로망을 이용한 헬리콥터 적응 비선형 제어)

  • Park, Bum-Jin;Hong, Chang-Ho;Suk, Jin-Young
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.32 no.4
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    • pp.24-33
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    • 2004
  • In this paper, the helicopter flight control system using online adaptive neural networks which have the universal function approximation property is considered. It is not compensation for modeling errors but approximation two functions required for feedback linearization control action from input/output of the system. To guarantee the tracking performance and the stability of the closed loop system replaced two nonlinear functions by two neural networks, weight update laws are provided by Lyapunov function and the simulation results in low speed flight mode verified the performance of the control system with the neural networks.

Direct Adaptive Fuzzy Control with Less Restrictions on the Control Gain

  • Phan, Phi Anh;Gale, Timothy J.
    • International Journal of Control, Automation, and Systems
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    • v.5 no.6
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    • pp.621-629
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    • 2007
  • In the adaptive fuzzy control field for affine nonlinear systems, there are two basic configurations: direct and indirect. It is well known that the direct configuration needs more restrictions on the control gain than the indirect configuration. In general, these restrictions are difficult to check in practice where mathematical models of plant are not available. In this paper, using a simple extension of the universal approximation theorem, we show that the only required constraint on the control gain is that its sign is known. The Lyapunov synthesis approach is used to guarantee the stability and convergence of the closed loop system. Finally, examples of an inverted pendulum and a magnet levitation system demonstrate the theoretical results.

Adaptive fuzzy sliding mode control (적응 퍼지 슬라이딩 모드 제어)

  • Yoo, Byung-Kook;Jeoung, Sa-Cheul;Ham, Woon-Chul
    • Journal of Institute of Control, Robotics and Systems
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    • v.2 no.4
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    • pp.287-296
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    • 1996
  • 본 논문에서는 퍼지추정기와 슬라이딩 모드제어이론이 고려되었다. 비선형시스템에 대한 슬라이딩 모드 제어기 설계 시에 그 시스템의 비선형함수를 추정하기 위하여 퍼지논리시스템이 사용되는 두가지의 적응처지슬라이딩 모드제어방식을 제안한다. 첫번째 방식에서는 비선형시스템, x/sup (n)/=f(x under bar, t) + b(x under bar, t)u 의 알지 못하는 함수 f를 추정하기 위하여 하나의 퍼지논리시스템이 사용되어진다. 두번째 방식에서는 비선형시스템의 f와 b에 대한 추정기로서의 두개의 퍼지논리시스템이 각각 사용되어진다. 각각의 방식에 대하여 제어시스템의 안정도를 보장하도록 하는 적응법칙을 설계하며 퍼지추정기와 비선형함수와의 추정오차를 줄이기 위해 각각에 대한 강인한 제어법칙을 제안한다. 제안된 네 가지의 제어법칙에 대한 안정성을 증명하고 컴퓨터시뮬레이션에서 역진자시스템에 적용하여 그에 대한 타당성과 각각의 비교를 보인다.

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