• 제목/요약/키워드: Lyapunov Function

검색결과 494건 처리시간 0.029초

다모선 전력계통에서 댐핑효과를 고려한 에너지 함수의 유도 (Derivation of an Energy Function Reflecting Damping Effects in Multi-Machine Power Systems)

  • 권용준;류헌수;최병곤;문영현
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2001년도 춘계학술대회 논문집 전력기술부문
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    • pp.172-175
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    • 2001
  • This paper presents a new energy function reflecting the damping effect in multi-machine power systems. The Lyapunov direct method provides precise and rigorous theoretical backgrounds for stability analysis of nonlinear systems. Incorporating damping effects into accurate estimates of the domain of attraction, which is a minor but crucial point, has been attempted with long history to yield partial success for single machine systems. In this paper, the damping-reflected energy function presented in the previous work has been generalized for application to multi-machine systems. The generalized energy function is tested for the WSCC 9-bus system to show the semi-negativeness of its time derivative.

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Tracking Control for Robot Manipulators based on Radial Basis Function Networks

  • Lee, Min-Jung;Park, Jin-Hyun;Jun, Hyang-Sig;Gahng, Myoung-Ho;Choi, Young-Kiu
    • 한국정보통신학회:학술대회논문집
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    • 한국해양정보통신학회 2005년도 춘계종합학술대회
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    • pp.285-288
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    • 2005
  • 신경회로망은 지능제어알고리즘 중의 하나로 학습능력을 가지고 있다. 이러한 학습능력 때문에 많은 분야에서 널리 사용되고 있으나, 지능제어의 단점인 안정도 문제를 수학적으로 증명하기 어렵다는 문제점을 갖고 있다. 본 논문에서는 신경회로망의 한 종류인 RBFN과 적응제어기법을 이용하여 로봇 매니퓰레이터 궤적 제어기를 구성하고 자 한다. 본 논문에서는 RBFN의 파라메터들을 적응제어기법을 이용하여 수학적으로 구하였고, 시스템의 안정도를 수학적으로 UUB를 만족한다는 것을 증명하였다. 그리고 수평다관절로봇 매니퓰레이터 궤적제어기에 적용하였다.

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구간시변 지연을 가지는 비선형시스템의 H 필터링 (H Filtering for a Class of Nonlinear Systems with Interval Time-varying Delay)

  • 이상문;유아연
    • 전기학회논문지
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    • 제63권4호
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    • pp.502-508
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    • 2014
  • In this paper, a delay-dependent $H_{\infty}$ filtering problem is investigated for discrete-time delayed nonlinear systems which include a more general sector nonlinear function instead of employing the commonly used Lipschitz-type function. By using the Lyapunov-Krasovskii functional approach, a less conservative sufficient condition is established for the existence of the desired filter, and then, the corresponding solvability condition guarantee the stability of the filter with a prescribed $H_{\infty}$ performance level. Finally, two simulation examples are given to show the effectiveness of the proposed filtering scheme.

모델 불확실성을 가지는 로봇 시스템을 위한 지능형 슬라이딩 모드 제어 (Intelligent Sliding Mode Control for Robots Systems with Model Uncertainties)

  • 유성진;최윤호;박진배
    • 제어로봇시스템학회논문지
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    • 제14권10호
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    • pp.1014-1021
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    • 2008
  • This paper proposes an intelligent sliding mode control method for robotic systems with the unknown bound of model uncertainties. In our control structure, the unknown bound of model uncertainties is used as the gain of the sliding controller. Then, we employ the function approximation technique to estimate the unknown nonlinear function including the width of boundary layer and the uncertainty bound of robotic systems. The adaptation laws for all parameters of the self-recurrent wavelet neural network and those for the reconstruction error compensator are derived from the Lyapunov stability theorem, which are used for an on-line control of robotic systems with model uncertainties and external disturbances. Accordingly, the proposed method can not only overcome the chattering phenomenon in the control effort but also have the robustness regardless of model uncertainties and external disturbances. Finally, simulation results for the five-link biped robot are included to illustrate the effectiveness of the proposed method.

Control of a Segway with unknown control coefficient and input constraint

  • Park, Bong Seok
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제16권2호
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    • pp.140-146
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    • 2016
  • This paper proposes a control method of the Segway with unknown control coefficient and input saturation. To design a simple controller for the Segway with the model uncertainty, the prescribed performance function is used. Furthermore, an auxiliary variable is introduced to deal with unknown time-varying control coefficient and input saturation problem. Due to the auxiliary variable, function approximators are not used in this paper although all model uncertainties are unknown. Thus, the controller can be simple. From the Lyapunov stability theory, it is proved that all errors of the proposed control system remain within the prescribed performance bounds. Finally, the simulation results are presented to demonstrate the performance of the proposed scheme.

Delay-dependent Guaranteed Cost Control for Uncertain Time Delay System

  • Lee, In-Beum;Choi, Jin-Young
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2001년도 ICCAS
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    • pp.62.4-62
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    • 2001
  • In this paper, we propose a delay-dependent guaranteed cost controller design method for uncertain linear systems with time delay. The uncertainty is norm bounded and time-varying. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, sufficient condition, which guarantees that the closed-loop system is asymptotically stable and the upper bound value of the closed-loop cost function is not more than a specied one, is derived in terms of Linear Matrix Inequalities(LMIs) that can be solved sufficiently. A convex optimization problem can be formulated to design a guaranteed cost controller, which minimizes the upper bound value of the cost function. Numerical examples show the activeness of the proposed method.

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Complexity Control Method of Chaos Dynamics in Recurrent Neural Networks

  • Sakai, Masao;Homma, Noriyasu;Abe, Kenichi
    • Transactions on Control, Automation and Systems Engineering
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    • 제4권2호
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    • pp.124-129
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    • 2002
  • This paper demonstrates that the largest Lyapunov exponent λ of recurrent neural networks can be controlled efficiently by a stochastic gradient method. An essential core of the proposed method is a novel stochastic approximate formulation of the Lyapunov exponent λ as a function of the network parameters such as connection weights and thresholds of neural activation functions. By a gradient method, a direct calculation to minimize a square error (λ - λ$\^$obj/)$^2$, where λ$\^$obj/ is a desired exponent value, needs gradients collection through time which are given by a recursive calculation from past to present values. The collection is computationally expensive and causes unstable control of the exponent for networks with chaotic dynamics because of chaotic instability. The stochastic formulation derived in this paper gives us an approximation of the gradients collection in a fashion without the recursive calculation. This approximation can realize not only a faster calculation of the gradient, but also stable control for chaotic dynamics. Due to the non-recursive calculation. without respect to the time evolutions, the running times of this approximation grow only about as N$^2$ compared to as N$\^$5/T that is of the direct calculation method. It is also shown by simulation studies that the approximation is a robust formulation for the network size and that proposed method can control the chaos dynamics in recurrent neural networks efficiently.

주파수 영역에서 반복 학습 제어의 수렴 조건 (Convergence Conditions of Iterative Learning Control in the Frequency Domain)

  • 도태용;문정호
    • 한국지능시스템학회논문지
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    • 제13권2호
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    • pp.175-179
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    • 2003
  • 반복 학습 제어에서 수렴 조건은 수렴 속도와 잔존 오차와 같은 성능을 결정한다. 따라서, 덜 신중한 수렴 조건을 구할 수 있다면, 그 성능은 향상될 것이고 사용 적합한 학습 제어기의 수는 증가된다. 주파수 영역에서, 연속적인 오차들간의 전달 함수의 $H_{\infty}$ 놈(norm)을 학습 시스템의 수렴성을 조사하기 위해 사용해왔다. 그러나, $H_{\infty}$ 놈을 바탕으로 한 수렴 조건이 단조 수렴성에 대하여 명확한 특성을 가진다하더라도, 특히, 다중 입출력 시스템에서 몇 가지 단점을 가진다. 본 논문에서 는 수렴 조건과 수렴의 단조성간의 관계를 밝힌다. 또한 주파수 영역에서 기존의 수렴 조건을 대신할 수 있는 수정된 수렴 조건을 주파수 영역 리아프노프(Lyapunov) 방정식을 이용하여 구한다.

삼중 덕티드 팬 비행체 운동모델링 및 리아푸노프 제어를 이용한 안정화 (Dynamic Modeling and Stabilization of a Tri-Ducted Fan Unmanned Aerial Vehicles using Lyapunov Control)

  • 나경석;원대희;윤석환;성상경;류민형;조진수;이영재
    • 한국항공우주학회지
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    • 제40권7호
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    • pp.574-581
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    • 2012
  • 로터를 이용한 무인비행체는 노출된 블레이드로 운용 시 위험이 따른다. 반면 덕티드팬은 블레이드 주위를 덕트로 감싸 위험요소를 줄여주고, 동일 동력 하중을 사용한 로터보다 향상된 추력성능을 보인다. 본 논문에서는 덕티드 팬의 장점을 적용하고자 세 개의 덕티드 팬으로 구성된 삼중 덕티드 팬 비행체 형상을 제안한다. 크기가 동일한 두 개의 덕티드 팬과, 크기가 다른 한 개의 덕티드 팬으로 구성되며 3개의 덕티드 팬 중 하나는 추력 방향 조절을 통해 신속한 자세 제어가 가능하다. 삼중 덕티드 팬 비행체의 운동방정식을 유도 하였고, 리아푸노프 함수를 적용하여 시스템을 안정하게 하는 제어 입력을 도출하였다. 그리고 비행체 초기모델의 파라미터를 적용하여 비선형 모델 시뮬레이션을 통해 안정한 자세각이 출력됨을 확인하고 결과를 분석하였다.

CONE VALUED LYAPUNOV TYPE STABILITY ANALYSIS OF NONLINEAR EQUATIONS

  • Chang, Sung-Kag;Oh, Young-Sun;An, Jeong-Hyang
    • 대한수학회지
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    • 제37권5호
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    • pp.835-847
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    • 2000
  • We investigate various ${\Phi}$(t)-stability of comparison differential equations and we obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f(t, x).

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