• Title/Summary/Keyword: Affine nonlinear system

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A piecewise affine approximation of sigmoid activation functions in multi-layered perceptrons and a comparison with a quantization scheme (다중계층 퍼셉트론 내 Sigmoid 활성함수의 구간 선형 근사와 양자화 근사와의 비교)

  • 윤병문;신요안
    • Journal of the Korean Institute of Telematics and Electronics C
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    • 제35C권2호
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    • pp.56-64
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    • 1998
  • Multi-layered perceptrons that are a nonlinear neural network model, have been widely used for various applications mainly thanks to good function approximation capability for nonlinear fuctions. However, for digital hardware implementation of the multi-layere perceptrons, the quantization scheme using "look-up tables (LUTs)" is commonly employed to handle nonlinear signmoid activation functions in the neworks, and thus requires large amount of storage to prevent unacceptable quantization errors. This paper is concerned with a new effective methodology for digital hardware implementation of multi-layered perceptrons, and proposes a "piecewise affine approximation" method in which input domain is divided into (small number of) sub-intervals and nonlinear sigmoid function is linearly approximated within each sub-interval. Using the proposed method, we develop an expression and an error backpropagation type learning algorithm for a multi-layered perceptron, and compare the performance with the quantization method through Monte Carlo simulations on XOR problems. Simulation results show that, in terms of learning convergece, the proposed method with a small number of sub-intervals significantly outperforms the quantization method with a very large storage requirement. We expect from these results that the proposed method can be utilized in digital system implementation to significantly reduce the storage requirement, quantization error, and learning time of the quantization method.quantization method.

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Robust Adaptive Neural Network Controller with Dynamic Structure for Nonaffine Nolinear Systems (불확실한 비선형 계통에 대한 동적인 구조를 가지는 강인한 적응 신경망 제어기 설계)

  • Park, Jang-Hyeon;Park, Gwi-Tae
    • Journal of Institute of Control, Robotics and Systems
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    • 제7권8호
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    • pp.647-655
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    • 2001
  • In adaptive neuro-control, neural networks are used to approximate unknown plant nonlinearities. Until now, most of the studies in the field of controller design for nonlinear system using neural network considers the affine system with fixed number of neurons. This paper considers nonaffine nonlinear systems and on-line variation of the number of neurons. A control law and adaptive laws for neural network weights are established so that the whole system is stable in the sense of Lyapunov. In addition, at the expense of th input, tracking error converges to the arbitrary small neighborhood of the origin. The efficiency of the proposed scheme is shown through simulations ofa simple nonaffine nonlinear system.

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Design of Robust Adaptive Fuzzy Controller for Uncertain Nonlinear System Using Estimation of Bounds for Approximation Errores and Dynamic Fuzzy Rule (근사화 오차의 유계상수 추정과 동적인 퍼지규칙을 이용한 비선형 계통에 대한 강인한 적응 퍼지 제어기 설계)

  • Park, Jang-Hyun;Seo, Ho-Joon;Park, Gwi-Tae
    • Proceedings of the KIEE Conference
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    • 대한전기학회 2000년도 하계학술대회 논문집 D
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    • pp.2308-2310
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    • 2000
  • In adaptive fuzzy control, fuzzy systems are used to approximate the unknown plant nonlinearities. Until now, most of the papers in the field of controller design for nonlinear system using fuzzy systems considers the affine system with fixed grid-rule structure. This paper considers general nonlinear systems and dynamic fuzzy rule structure. Adaptive laws for fuzzy parameters and fuzzy rule structrue are established so that the whole system is stable in the sense of Lyapunov.

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A Study on the System Identification based on Neural Network for Modeling of 5.1. Engines (S.I. 엔진 모델링을 위한 신경회로망 기반의 시스템 식별에 관한 연구)

  • 윤마루;박승범;선우명호;이승종
    • Transactions of the Korean Society of Automotive Engineers
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    • 제10권5호
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    • pp.29-34
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    • 2002
  • This study presents the process of the continuous-time system identification for unknown nonlinear systems. The Radial Basis Function(RBF) error filtering identification model is introduced at first. This identification scheme includes RBF network to approximate unknown function of nonlinear system which is structured by affine form. The neural network is trained by the adaptive law based on Lyapunov synthesis method. The identification scheme is applied to engine and the performance of RBF error filtering Identification model is verified by the simulation with a three-state engine model. The simulation results have revealed that the values of the estimated function show favorable agreement with the real values of the engine model. The introduced identification scheme can be effectively applied to model-based nonlinear control.

Nonlinear ANC system robust to background noise variation by using 3rd-order Volterra filtering with a VSSGS-PAP algorithm (3차 볼테라 필터링과 VSSGS-PAP 알고리즘을 이용한 배경잡음 변화에 강인한 비선형 능동소음제어 시스템)

  • Seo, Jae-Beom;Kim, Kyoung-Jae;Nam, Sang-Won
    • Proceedings of the IEEK Conference
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    • 대한전자공학회 2009년도 정보 및 제어 심포지움 논문집
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    • pp.70-72
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    • 2009
  • In this paper, nonlinear active noise control(ANC) of a 3rd-order Volterra system, which is robust to background noise variation, is proposed along with a variable step-size Gauss-Seidel pseudo affine projection(VSSGS-PAP) algorithm. Simulation results demonstrate that the proposed approach yields better nonlinear ANC performance in a background noise variation environment, compared with the conventional methods for the nonlinear ANC.

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Voltage Controller Design of Synchronous Generator by Pole Assignment (극배치에 의한 동기발전기의 전압제어기 설계)

  • Yim, Han-Suck
    • The Transactions of the Korean Institute of Electrical Engineers
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    • 제34권12호
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    • pp.472-484
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    • 1985
  • A design of robust voltage controller for high speed excitation of synchronous machine was carried out by pole assignment techniques. An affine map from characteristic polynomial coefficients to feedback parameters is formulated in order to place the system eigen values in the desired region. The feedback parameters determined from linearized model are tested on nonlinear model subjecting it to small disturbances and system faults to show the effectiveness of the controller designed by the proposed technique. The results obtained indicate that the controller presented improves the dynamic stability and system performances of conventionally controlled synchronous machine significantly.

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Design of Robust Adaptive Fuzzy Controller for Uncertain Nonlinear System Using Estimation of Bounding Constans and Dynamic Fuzzy Rule Insertion (유계상수 추정과 동적인 퍼지 규칙 삽입을 이용한 비선형 계통에 대한 강인한 적응 퍼지 제어기 설계)

  • Park, Jang-Hyun;Park, Gwi-Tae
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • 제50권1호
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    • pp.14-21
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    • 2001
  • This paper proposes an indirect adaptive fuzzy controller for general SISO nonlinear systems. In indirect adaptive fuzzy control, based on the proved approximation capability of fuzzy systems, they are used to capture the unknown nonlinearities of the plant. Until now, most of the papers in the field of controller design for nonlinear system considers the affine system using fuzzy systems which have fixed grid-rule structure. We proposes a dynamic fuzzy rule insertion scheme where fuzzy rule-base grows as time goes on. With this method, the dynamic order of the controller reduces dramatically and an appropriate number of fuzzy rules are found on-line. 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.

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A fuzzy-model-based controller for a helicopter system with 2 degree-of-freedom in motion (2 자유도 헬리콥터 시스템의 제어를 위한 퍼지 모델 기반 제어기)

  • Chang, Wook;Lee, Ho-Jae;Joo, Young-Hoon;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • 대한전기학회 2001년도 하계학술대회 논문집 D
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    • pp.1949-1951
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    • 2001
  • This paper deals with the control of a nonlinear experimental helicopter system by using the fuzzy-model-based control approach. The fuzzy model of the experimental helicopter system is constructed from the original nonlinear dynamic equations in the form of an affine Takagi-Sugeno (TS) fuzzy system. In order to design a feasible switching-type fuzzy-model-based controller, the TS fuzzy system is converted to a set of uncertain linear systems, which is used as a basic framework to synthesize the fuzzy-model-based controller.

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Design of Fuzzy Observer for Nonlinear System using Dynamic Rule Insertion (비선형 시스템에 대한 동적인 규칙 삽입을 이용한 퍼지 관측기 설계)

  • Seo, Ho-Joon;Park, Jang-Hyun;Seo, Sam-Jun;Kim, Dong-Sik;Park, Gwi-Tae
    • Proceedings of the KIEE Conference
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    • 대한전기학회 2001년도 하계학술대회 논문집 D
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    • pp.2308-2310
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    • 2001
  • In the adaptive fuzzy sliding mode control, from a set of a fuzzy IF-THEN rules adaptive fuzzy sliding mode control whose parameters are adjusted on-line according to some adaptation laws is constructed for the purpose of controlling the plant to track a desired trajectory. Most of the research works in nonlinear controller design using fuzzy systems consider the affine system with fixed grid-rule structure based on system state availability. The fixed grid-rule structure makes the order of the controller big unnecessarily, hence the on-line fuzzy rule structure and fuzzy observer based adaptive fuzzy sliding mode controller is proposed to solve system state availability problems. Therefore, adaptive laws of fuzzy parameters for state observer and fuzzy rule structure are established implying whole system stability in the sense of Lyapunov.

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Observer Based Sliding Mode Controller for Nonlinear System using Dynamic Rule Insertion

  • Seo, Ho-Joon;Kim, Dong-Sik;Seo, Sam-Jun;Park, Jang-Hyun;Park, Gwi-Tae
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2001년도 ICCAS
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    • pp.67.2-67
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    • 2001
  • In the adaptive fuzzy sliding mode control, from a set of fuzzy IF-THEN rules adaptive fuzzy sliding mode control whose parameters are adjusted on-line according to some adaptation laws is constructed for the purpose of controlling the plant to track a desired trajectory. Most of the research works in nonlinear controller design using fuzzy systems consider the affine system with fixed grid-rule structure based on system state availability. The fixed grid-rule structure makes the order of the controller big unnecessarily, hence the on-line fuzzy rule structure and fuzzy observer based adaptive fuzzy sliding mode controller is proposed to solve system state availability problems. Therefore adaptive laws of fuzzy parameters ...

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