• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.251-266
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• 2004

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forces $Q_1$ and the restrictions for the perturbations $Q_2$ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 심포지엄 논문집 정보 및 제어부문
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• pp.13-15
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• 2004

In this paper, we propose a novel stability criterion and a guideline of controller design for switched linear systems. Unlike existing criterions such as Lie algebraic method and multiple Lyapunov functions method, the proposed criterion can be applied to each individual system without considering an overall system. By applying the proposed criterion to each individual system separately, a state feedback controller can be easily designed. Stability of the overall system is proved by developing a rule to determine non-increasing Lyapunov functions recursively at each switching instant. An illustrative example is given.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.387-392
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• 2004

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.

• 한국정밀공학회지
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• 제15권12호
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• pp.226-235
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• 1998

This study proposes the analysis and evaluation of method of time series of ultrasonic signal using the chaotic feature extraction for ultrasonic pattern recognition. The features are extracted from time series data for analysis of weld defects quantitatively. For this purpose, analysis objectives in this study are fractal dimension, Lyapunov exponent, and strange attractor on hyperspace. The Lyapunov exponent is a measure of rate in which phase space diverges nearby trajectories. Chaotic trajectories have at least one positive Lyapunov exponent, and the fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal(correlation) dimensions and Lyapunov exponents show the mean value of 4.663, and 0.093 relatively in case of learning, while the mean value of 4.926, and 0.090 in case of testing in slag inclusion(weld defects) are shown. Therefore, the proposed chaotic feature extraction can be enhancement of precision rate for ultrasonic pattern recognition in defecting signals of weld zone, such as slag inclusion.

• 한국정보통신학회논문지
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• 제13권8호
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• pp.1647-1652
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• 2009

비선형 동력학 시스템으로 구성된 전력 수요의 시계열 데이터를 예측하기 위해 적용된 신경망 및 퍼지 적응 알고리즘 등은 예측오차가 상대적으로 크게 나타났다. 이는 전력수요 시계열 데이터가 가지고 있는 카오스적인 성질에 기인하며 이중 초기값에 민감한 의존성은 장기적인 예측을 더욱더 어렵게 하는 요인으로 작용한다. 전력수요 시계열 데이터가 가지고 있는 카오스적인 성질을 정량 및 정성적인 방식으로 분석 을 수행하고, 시스템 동력학적 특성의 정량분석에 이용되는 Lyapunov 지수를 이용하여 어트랙터 재구성, 다차원 카오스 시계열 데이터를 예측하는 방식으로 수요예측 시뮬레이션을 수행하고 결과를 비교 평가하여 기존 제안방식보다 실용적이며 효과적임을 확인한다.

• 제어로봇시스템학회논문지
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• 제12권5호
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• pp.411-418
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• 2006

There are mainly two types of bang-bang controllers for nominal linear time-invariant (LTI) system. Optimal bang-bang controller is designed based on optimal control theory and suboptimal bang-bang controller is obtained by using Lyapunov stability condition. In this paper, the suboptimal bang-bang control method is extended to LTI system involving both control input saturation and structured real parameter uncertainties by using Lyapunov robust stability condition. Two robust optimal bang-bang controllers are derived by minimizing the time derivative of Lyapunov function subjected to the limit of control input. The one is developed based on the classical quadratic stability(QS), and the other is developed based on the affine quadratic stability(AQS). And characteristics of the two controllers are compared. Especially, bounds of parameter uncertainties which theoretically guarantee robust stability of the two controllers are compared quantitatively for 1DOF vibrating system. Moreover, the validity of robust optimal bang-bang controller based on the AQS is shown through numerical simulations for this system.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2009년도 춘계학술대회
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• pp.171-174
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• 2009

비선형 동력학 시스템으로 구성된 전력 수요의 시계열 데이터를 예측하기 위해 적용된 신경망 및 퍼지 적응 알고리즘 등은 예측오차가 상대적으로 크게 나타났다. 이는 전력수요 시계열 데이터가 가지고 있는 카오스적인 성질에 기인하며 이중 초기값에 민감한 의존성은 장기적인 예측을 더욱더 어렵게 하는 요인으로 작용한다. 전력수요 시계열 데이터가 가지고 있는 카오스적인 성질을 정량 및 정성적인 방식으로 분석을 수행하고, 시스템 동력학적 특성의 정량분석에 이용되는 Lyapunov 지수를 이용하여 어트랙터 재구성, 다차원 카오스 시계열 데이터를 예측하는 방식으로 수요예측 시뮬레이션을 수행하고 결과를 비교 평가하여 기존 제안방식보다 실용적이며 효과적임을 확인한다.

• 대한임베디드공학회논문지
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• 제16권4호
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• pp.119-127
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• 2021

The aim of this paper is to propose a less conservative stabilization condition for leader-following sampled-data control of wheeled mobile robot (WMR) systems by using a clock-dependent Lyapunov function (CDLF) with looped functionals. In the leader-following WMR system, the state and input of the leader robot are measured by digital devices mounted on the following robot, and they are utilized to construct the sampled-data controller of the following robot. To design the sampled-data controller, a stabilization condition is derived by using the CDLF with looped functionals, and formulated in terms of sum of squares (SOS). The considered Lyapunov function is a polynomial form with respect to the clock related to the transmitted sampling instants. As the degree of the Lyapunov function increases, the stabilization condition becomes less conservative. This ensures that the designed controller is able to stabilize the system with a larger maximum sampling interval. The simulation results are provided to demonstrate the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1744-1746
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• 2004

This paper focuses on the problem of asymptotic stabilization for time-delay systems. To this end, a memoryless state feedback controller is proposed. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Certain free weighting matrices are used to express this relationship and linear matrix inequalities (LMIs)-based algorithm to design the controller stabilizing the system.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.297-303
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• 2001

In this paper, the problem of the stability analysis for a class of linear neutral systems with time-varying delay is investigated. Using the Lyapunov method, a delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs) is presented. The LMIs can be easily solved by various convex optimization algorithms.