• 제목/요약/키워드: Lyapunov's function

검색결과 108건 처리시간 0.028초

리아프노프 함수를 이용한 Chua 오실레이터 회로에서의 카오스 제어 (A Study on Chaos Control of a Chua' Oscillator Circuit Using a Lyapunov function)

  • 배영철;고재호;유창환;홍대승;임화영
    • 한국정보통신학회논문지
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    • 제3권1호
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    • pp.113-120
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    • 1999
  • Chua 발진기의 카오스 신호를 선형 상태 피드백 제어 이론을 적용하여 평형점, 1주기, 2주기의 신호로 제어하는 방법을 제안하였다. 제안한 선형 상태 피드백 이득 값을 리아프노프 함수를 이용하여 Chua 오실레이터가 나타내는 모든 카오스 현상을 제어할 수 있도록 파라미터 부호의 조합에 의해 4가지로 분류하였다. 본 논문의 상태 피드백 제어 기법은 시스템의 카오스 상태에서 얻고자 하는 상태(평형점, 주기 신호등)로 효율적으로 제어 가능하고, 매우 간단한 구조로 파라미터의 변화 없이 최소의 입력으로 가능케 하였다.

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Designing an Emotional Intelligent Controller for IPFC to Improve the Transient Stability Based on Energy Function

  • Jafari, Ehsan;Marjanian, Ali;Solaymani, Soodabeh;Shahgholian, Ghazanfar
    • Journal of Electrical Engineering and Technology
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    • 제8권3호
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    • pp.478-489
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    • 2013
  • The controllability and stability of power systems can be increased by Flexible AC Transmission Devices (FACTs). One of the FACTs devices is Interline Power-Flow Controller (IPFC) by which the voltage stability, dynamic stability and transient stability of power systems can be improved. In the present paper, the convenient operation and control of IPFC for transient stability improvement are considered. Considering that the system's Lyapunov energy function is a relevant tool to study the stability affair. IPFC energy function optimization has been used in order to access the maximum of transient stability margin. In order to control IPFC, a Brain Emotional Learning Based Intelligent Controller (BELBIC) and PI controller have been used. The utilization of the new controller is based on the emotion-processing mechanism in the brain and is essentially an action selection, which is based on sensory inputs and emotional cues. This intelligent control is based on the limbic system of the mammalian brain. Simulation confirms the ability of BELBIC controller compared with conventional PI controller. The designing results have been studied by the simulation of a single-machine system with infinite bus (SMIB) and another standard 9-buses system (Anderson and Fouad, 1977).

신경회로망 기반의 적응제어기를 이용한 AUV의 운동 제어 (Motion Control of an AUV Using a Neural-Net Based Adaptive Controller)

  • 이계홍;이판묵;이상정
    • 한국해양공학회지
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    • 제16권1호
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    • pp.8-15
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    • 2002
  • This paper presents a neural net based nonlinear adaptive controller for an autonomous underwater vehicle (AUV). AUV's dynamics are highly nonlinear and their hydrodynamic coefficients vary with different operational conditions, so it is necessary for the high performance control system of an AUV to have the capacities of learning and adapting to the change of the AUV's dynamics. In this paper a linearly parameterized neural network is used to approximate the uncertainties of the AUV's dynamic, and the basis function vector of network is constructed according to th AUV's physical properties. A sliding mode control scheme is introduced to attenuate the effect of the neural network's reconstruction errors and the disturbances in AUV's dynamics. Using Lyapunov theory, the stability of the presented control system is guaranteed as well as the uniformly boundedness of tracking errors and neural network's weights estimation errors. Finally, numerical simulations for motion control of an AUV are performed to illustrate the effectiveness of the proposed techniques.

특이섭동을 포함한 타카기 - 수게노 형태의 비선형 시스템을 위한 새로운 샘플치 제어기의 설계기법 제안 (Sampled-Data Controller Design for Nonlinear Systems Including Singular Perturbation in Takagi-Sugeno Form)

  • 문지현;이재준;이호재
    • 한국지능시스템학회논문지
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    • 제26권1호
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    • pp.50-55
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    • 2016
  • 본 논문은 특이섭동을 포함한 비선형 시스템을 위한 샘플치 제어 기법을 논한다. 비선형 시스템은 타카기--수게노(Takagi--Sugeno: T--S) 퍼지모델 형태로 표현됨을 가정한다. 새로운 리아푸노프 함수와 추가적인 항등식을 이용하여 선형행렬부등식 형태의 샘플치 폐루프 T--S 퍼지시스템의 점근적 안정도 조건을 제시한다. 분석결과에 대한 몇 가지 논의점을 언급한다. 모의실험에 의하여 제안된 기법의 타당성을 보인다.

시변 지연이 있는 비선형 시스템에 대한 $H_{\infty}$ 퍼지 강인제어기 설계 (Static Output Feedback Robust $H_{\infty}$ Fuzzy Control of Nonlinear Systems with Time-Varying Delay)

  • 김택룡;박진배;주영훈
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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    • pp.379-381
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    • 2004
  • In this paper, a robust $H_{\infty}$ stabilization problem to a uncertain fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H_{\infty}$ controllers are given in terms of linear matrix inequalities.

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System model reduction by weighted component cost analysis

  • Kim, Jae-Hoon;Skelton, Robert-E.
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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    • pp.524-529
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    • 1993
  • Component Cost Analysis considers any given system driven by a white noise process as an interconnection of different components, and assigns a metric called "component cost" to each component. These component costs measure the contribution of each component to a predefined quadratic cost function. One possible use of component costs is for model reduction by deleting those components that have the smallest component cost. The theory of Component Cost Analysis is extended to include finite-bandwidth colored noises. The results also apply when actuators have dynamics of their own. When the dynamics of this input are added to the plant, which is to be reduced by CCA, the algorithm for model reduction process will be called Weighted Component Cost Analysis (WCCA). Closed-form analytical expressions of component costs for continuous time case, are also derived for a mechanical system described by its modal data. This is very useful to compute the modal costs of very high order systems beyond Lyapunov solvable dimension. A numerical example for NASA's MINIMAST system is presented.presented.

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시변지연을 가지는 TS퍼지시스템을 위한 견실 시간종속 안정성판별법 (Robust Delay-dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Time-varying Delay)

  • 유아연;이상문;권오민
    • 전기학회논문지
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    • 제64권6호
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    • pp.891-899
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    • 2015
  • This paper presents the robust stability condition of uncertain Takagi-Sugeno(T-S) fuzzy systems with time-varying delay. New augmented Lyapunov-Krasovskii function is constructed to ensure that the system with time-varying delay is globally asymptotically stable. Also, less conservative delay-dependent stability criteria are obtained by employing some integral inequality, reciprocally convex approach and new delay-partitioning method. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

완화된 Non-Quadratic 안정화 조건을 기반으로 한 이산 시간 Takagi-Sugeno 퍼지 시스템의 최적 제어 (Optimal Control for Discrete-Time Takagi-Sugeno Fuzzy Systems Based on Relaxed Non-Quadratic Stabilization Conditions)

  • 이동환;박진배;양한진;주영훈
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2009년도 제40회 하계학술대회
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    • pp.1724_1725
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    • 2009
  • In this paper, new approaches to optimal controller design for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems are proposed based on a relaxed approach, in which non-quadratic Lyapunov function and non-parallel distributed compensation (PDC) control law are used. New relaxed conditions and linear matrix inequality (LMI) based design methods are proposed that allow outperforming previous results found in the literature. Finally, an example is given to demonstrate the efficiency of the proposed approaches.

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퍼지 기법을 이용한 시간 지연을 가지는 이산시간 비선형 시스템에 대한 강인 제어기 설계 (Design of the Robust Controller for the Discrete-Time Nonlinear System with Time-Delay Via Fuzzy Approach)

  • 김택룡;박진배;주영혼
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2005년도 제36회 하계학술대회 논문집 D
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    • pp.2723-2725
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    • 2005
  • In this paper, a robust $H{\infty}$ stabilization problem to a uncertain discrete-time nonlinear systems with time-delay via fuzzy static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-delayed state. Then parallel distributed compensation technique is used for designing of the robust fuzzy controller. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H{\infty}$ controllers are given in terms of linear matrix inequalities via similarity transform and congruence transform technique.

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QLQG/$H_{\infty}$ 제어를 이용한 다변수 하드비선형 제어기 설계 (Design of the multivariable hard nonlinear controller using QLQG/$H_{\infty}$ control)

  • 한성익;김종식
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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    • pp.81-84
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    • 1996
  • We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

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