• The Transactions of the Korean Institute of Power Electronics
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• v.20 no.4
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• pp.344-350
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• 2015

A battery management system requires accurate information on the battery state of charge (SOC) to achieve efficient energy management of electric vehicle and renewable energy systems. Although correct SOC estimation is difficult because of the changes in the electrical characteristics of the battery attributed to ambient temperature, service life, and operating point, various methods for accurate SOC estimation have been reported. On the basis of piecewise linear (PWL) modeling technique, this paper proposes a simple SOC observer for lithium-polymer batteries. For performance evaluation, the SOC estimated by the PWL SOC observer, the SOC measured by the battery-discharging experiment and the SOC estimated by the extended Kalman filter (EKF) estimator were compared through a PSIM simulation study.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.499-499
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• 2000

The robust stability problems for nominally linear system with nonlinear, structured perturbations arc considered with Lyapunov direct method. The Lyapunov direct method has been utilized to determine the bounds for nonlinear, time-dependent functions which can be tolerated by a stable nominal system. In most cases quadratic forms are used either as components of vector Lyapunov function or as a function itself. The resulting estimates are usually conservative. As it is known, often the conservatism of the bounds we propose to use a piecewise quadratic Lyapunov function. An example demonstrates application of the proposed method.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.4
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• pp.53-62
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• 2009

Lee[15] examined quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model where quantity discounts are provided based on the previous order size. During the two periods, the retailer faces stochastic (truncated Poisson distributed) demands and he/she places orders to meet the demands. The manufacturer provides for the retailer a price discount for the second period order if its quantity exceeds the first period order quantity. In this paper we extend the above two-period model to a k-period one (where k < 2) and propose a stochastic nonlinear mixed binary integer program for it. In order to make the program tractable, the nonlinear term involving the sum of truncated Poisson cumulative probability function values over a certain range of demand is approximated by an i-interval piecewise linear function. With the value of i selected and fixed, the piecewise linear function is determined using an evolutionary algorithm where its fitness to the original nonlinear term is maximized. The resulting piecewise linear mixed binary integer program is then transformed to a mixed binary integer linear program. With the k-period model developed, we suggest a solution procedure of receding horizon control style to solve n-period (n < k) order decision problems. We implement Lee's two-period model and the proposed k-period model for the use in receding horizon control style to solve n-period order decision problems, and compare between the two models in terms of the pattern of order quantities and the total profits. Our computational study shows that the proposed model is superior to the two-period model with respect to the total profits, and that order quantities from the proposed model have higher fluctuations over periods.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.787-800
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• 2000

In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.922-931
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• 2011

An efficient calibration algorithm for mobile robot localization using infrared range finder is proposed. A calibration is important to guarantee the performance of other algorithms which use sensor data because it is pre-process. We experimentally found that the infrared range finder PBS-03JN has error characteristics depending on both distance and scan angle. After obtaining 2-D grid error characteristic data on distance and scan angle, we proposed a simple and efficient calibration algorithm with a 2-D piecewise linear function set. The performance of our proposed calibration algorithm is verified by experiments and simulation.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1506-1509
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• 1999

This paper presents a new economic dispatch algorithm to improve the unit commitment solution while guaranteeing the near optimal solution without reducing calculation speed. The conventional economic dispatch algorithms have the problem that it is not applicable to the unit commitment formulation due to the frequent on/off state changes of units during the unit commitment calculation. Therefore, piecewise linear iterative method have generally been used for economic dispatch algorithm for unit commitment. In that method, the approximation of the generator cost function makes it hard to obtain the optimal economic dispatch solution. In this case, the solution can be improved by introducing a inverse of the incremental cost function. The proposed method is tested with sample system. The results are compared with the conventional piecewise linear iterative method. It is shown that the proposed algorithm yields more accurate and economical solution without calculation speed reduction.

• East Asian mathematical journal
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• v.30 no.5
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• pp.583-597
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• 2014

In this paper, we study an area-preserving piecewise linear map with the feature of dangerous border collision bifurcations. Using this map, we study dynamical properties occurred in the invariant set, specially related to the boundary of KAM-tori, and the existence and stabilities of periodic orbits. The result shows that elliptic regions having periodic orbits and chaotic region can be divided by smooth curve, which is an unexpected result occurred in area preserving smooth dynamical systems.