• 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 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 Electrical Engineering and Technology
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• v.4 no.3
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• pp.353-359
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• 2009

This paper proposes a novel technique for calculating the security costs that properly includes ramping constraints in the operation of a deregulated power system. The ramping process is modeled by a piecewise linear function with certain assumptions. During this process, a ramping cost is incurred if the permissible limits are exceeded. The optimal production costs of the power producers are calculated with the ramping cost included, considering a time horizon with N-1 contingency cases using contingency constrained optimal power flow (CCOPF), which is solved by the primal-dual interior point method (PDIPM). A contingency analysis is also performed taking into account the severity index of transmission line outages and its sensitivity analysis. The results from an illustrative case study based on the IEEE 30-bus system are analyzed. One attractive feature of the proposed approach is that an optimal solution is more realistic than the conventional approach because it satisfies physical constraints, such as the ramping constraint.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.1
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• pp.200-220
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• 2016

Orthogonal frequency division multiplexing (OFDM) signals suffer from the problem of large peak-to-average power ratio (PAPR) which complicates the design of the analog front-end of the system. Companding is a well-known PAPR reduction technique that reduces the PAPR by transforming the signal amplitude using a deterministic function. In this paper, a novel piecewise linear companding transform is proposed. The design criteria for the proposed transform is developed by investigating the relationships between the compander and decompander's profile and parameters with the system's performance metrics. Using analysis and simulations, we relate the companding parameters with the bit error rate (BER), out-of-band interference (OBI), amount of companding noise, computational complexity and average power. Based on a set of criteria developed thereof, we formulate the design of the proposed transform. The main aim is to preserve the signal's attributes as much as possible for a predetermined amount of PAPR reduction. Simulations are carried out to evaluate and compare the proposed scheme with the existing companding transforms to demonstrate the enhancement in PAPR, BER and OBI performances.

• 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.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.2
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• pp.9-17
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• 2010

Recently, there has been much interest in orthogonal frequency division multiplexing (OFDM) for next generation wireless wideband communication systems. OFDM is a special case of multicarrier transmission, where a single data stream is transmitted over a number of lower-rate subcarriers. One of the main reasons to use OFDM is to increase robustness against frequency-selective fading or narrowband interference. However, in the radio systems it is also important to distortion introduced by high power amplifiers (HPA's) such as solid state power amplifier (SSPA) considered in this paper. Since the signal amplitude of the OFDM system is Rayleigh-distributed, the performance of the OFDM system is significantly degraded by the nonlinearity of the HPA in the OFDM transmitter. In this paper, we propose a canonical piecewise-linear (PWL) model based digital predistorter to prevent signal distortion and spectral re-growth due to the high peak-to-average power ratio (PAPR) of OFDM signal and the nonlinearity of HPA's. Computer simulation on an OFDM system under additive white Gaussian noise (AWGN) channels with QPSK, 16-QAM and 64-QAM modulation schemes and modulator/demodulator implemented with 1024-point FFT/IFFT, demonstrate that the proposed predistorter achieves significant performance improvement by effectively compensating for the nonlinearity introduced by the SSPA.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.1
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• pp.26-36
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• 2021

The topic of this study is the field of humanitarian logistics for disaster response. Many existing studies have revealed that compliance with the golden time in response to a disaster determines the success or failure of relief activities, and logistics costs account for 80% of the disaster response cost. Besides, the agility, responsiveness, and effectiveness of the humanitarian logistics system are emphasized in consideration of the disaster situation's characteristics, such as the urgency of life-saving and rapid environmental changes. In other words, they emphasize the importance of logistics activities in disaster response, which includes the effective and efficient distribution of relief supplies. This study proposes a mathematical model for establishing a transport plan to distribute relief supplies in a disaster situation. To determine vehicles' route and the amount of relief for cities suffering a disaster, it mainly considers the urgency, effectiveness (restoration rate), and uncertainty in the logistics system. The model is initially developed as a mixed-integer nonlinear programming (MINLP) model containing some nonlinear functions and transform into a Mixed-integer linear programming (MILP) model using a logarithmic transformation and piecewise linear approximation method. Furthermore, a minimax problem is suggested to search for breakpoints and slopes to define a piecewise linear function that minimizes the linear approximation error. A numerical experiment is performed to verify the MILP model, and linear approximation error is also analyzed in the experiment.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.169-172
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• 1999

In this paper, piecewise quadratic Lyapunov functions are used to analyze the stability of fuzzy-model-based controller. We represent the nonlinear system using a Takagi-Sugeno fuzzy model, which represent the given nonlinear system by fuzzy inference rules and local linear dynamic models. The proposed stability analysis technique is developed by dividing the whole fuzzy system into the smaller separate fuzry systems to reduce the conservatism. Some necessary and sufficient conditions for the proposed method are obtained. Finally, stability of the closed system with various kinds of controller for TS fuzzy model is checked through the proposed method.

• Journal of the Korean GEO-environmental Society
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• v.9 no.6
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• pp.53-60
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• 2008

In recent years, finite strain consolidation theories including a mechanical nonlinearity and a reasonable coordinate system have been proposed and used in educations and practical consolidation problems. However, despite their reasonable ability to predict the consolidation behavior, their failure in the field can be attributed to the complexity of estimating and selecting proper parameters for simulating the consolidation phenomenon. In this study, therefore, the application of a piecewise-linear method was proposed to solve such problems including the assumption of the uniqueness in compressibility. Especially, the concept of reference curve was introduced to define the effect of strain rate dependency of clay. The applicability of the methodology is verified by several tests. It was found that the proposed method is applicable in restrictive ranges of study carried out in the laboratory. Finally it is expected that the verification in field consolidation problem has to be carried out through future study.