• 대한수학회보
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• 제35권3호
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• pp.473-484
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• 1998

We consider a finite difference approximation to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is proved that the rate of convergence is $O(h^2)$. To obtain the solution of the finite difference equation, an iterative scheme converging monotonically to the solution of the finite difference equation is introduced. And the numerical experiment of this method is given.

• International Journal of Control, Automation, and Systems
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• 제4권2호
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• pp.146-154
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• 2006

In this paper, we propose direct and indirect adaptive fuzzy sliding mode control approaches for a class of nonaffine nonlinear systems. In the direct case, we use the implicit function theory to prove the existence of an ideal implicit feedback linearization controller, and hence approximate it to attain the desired performances. In the indirect case, we exploit the linear structure of a Takagi-Sugeno fuzzy system with constant conclusion to establish an affine-in-control model, and therefore design an indirect adaptive fuzzy controller. In both cases, the adaptation laws of the adjustable parameters are deduced from the stability analysis, in the sense of Lyapunov, to get a more accurate approximation level. In addition to their robustness, the design of the proposed approaches does not require the upper bounds of both external disturbances and approximation errors. To show the efficiency of the proposed controllers, a simulation example is presented.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.1-14
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• 2008

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and $Gr\ddot{u}nwald$-Letnikov(G-L) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
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• pp.10-13
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• 2001

Nonlinear Function Approximation of Moduled Neural Network Using Genetic Algorithm Neural Network consists of neuron and synapse. Synapse memorize last pattern and study new pattern. When Neural Network learn new pattern, it tend to forget previously learned pattern. This phenomenon is called to catastrophic inference or catastrophic forgetting. To overcome this phenomenon, Neural Network must be modularized. In this paper, we propose Moduled Neural Network. Modular Neural Network consists of two Neural Network. Each Network individually study different pattern and their outputs is finally summed by net function. Sometimes Neural Network don't find global minimum, but find local minimum. To find global minimum we use Genetic Algorithm.

• 대한수학회보
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• 제51권1호
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• pp.189-206
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• 2014

In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation $$u_{tt}-M({\parallel}{\nabla}u{\parallel}^2){\triangle}u+{\alpha}u_t+f(u)=0\;in\;{\Omega}{\times}[0,{\infty}),\\u(x,t)=0\;on\;{\Gamma}_1{\times}[0,{\infty}),\\{\frac{{\partial}u}{\partial{\nu}}}+g(u_t)=0\;on\;{\Gamma}_0{\times}[0,{\infty}),\\u(x,0)=u_0,u_t(x,0)=u_1\;in\;{\Omega}$$ with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. [33]. Furthermore,we overcome some difficulties due to the presence of nonlinear terms $M({\parallel}{\nabla}u{\parallel}^2)$ and $g(u_t)$ by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년 학술대회 논문집 정보 및 제어부문
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• pp.220-222
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• 2006

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated lineal operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a T-S fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.

• 전자공학회논문지B
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• 제32B권5호
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• pp.812-820
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• 1995

This paper proposes an approach of identifying nonlinear mappings from input/output data. The approach is based on the universal approximation by the fuzzy integration of local affine mappings. A connectionist model realizing the universal approximator is suggested by using a processing unit based on both the radial basis function and the weighted sum scheme. In addition, a learning method with self-organizing capability is proposed for the identifying of nonlinear mapping relationships with the given input/output data. To show the effectiveness of our approach, the proposed model is applied to the function approximation and the prediction of Mackey-Glass chaotic time series, and the performances are compared with other approaches.

• 한국항행학회논문지
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• 제7권1호
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• pp.14-21
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• 2003

장거리 $3{\times}40$ Gbps 강도 변조 직접 검파 방식의 파장 분할 다중 시스템에서 색 분산과 자기 위상 변조에 의한 광 펄스 왜곡을 최상으로 보상할 수 있는 최적의 펌프 전력을 컴퓨터 시뮬레이션을 통해 살펴보았다. 본 논문에서 고찰한 파장 분할 다중 시스템은 전체 전송로 중간에 HNL-DSF (highly nonlinear dispersion shifted fiber)의 광 위상 공액기를 두어 광 신호 왜곡을 보상하는 경로 평균 강도 근사 (PAIA : Path-Averaged Intensity Approximation) 기법의 MSSI (Mid-Span Spectral Inversion)가 적용된 시스템이다. 우선 HNL-DSF는 광대역 파장 분할 다중 전송에서 매우 유용한 비선형 매질이라는 것을 확인할 수 있었고, 두 번째 광 전송로로 입사되는 공액파의 전력을 입력 광 신호의 전력과 같아지게 하는 HNL-DSF 광 위상 공액기의 펌프 전력에서 최상의 보상이 얻어지는 것을 확인할 수 있었다. 결과적으로 PAIA MSSI 기법에 전송 거리에 관계한 최적 펌프 전력을 갖는 HNL-DSF 광 위상 공액기를 적용하면 장거리 대용량 파장 분할 다중 시스템의 구현이 가능하다는 것을 확인할 수 있었다.

• 지구물리와물리탐사
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• 제7권1호
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• pp.51-55
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• 2004

This paper presents a fast and stable imaging scheme using the localized nonlinear (LN) approximation of integral equation (IE) solutions for inverting electromagnetic data obtained in a crosswell survey. The medium is assumed to be cylindrically symmetric about a source borehole, and to maintain the symmetry a vertical magnetic dipole is used as a source. To find an optimum balance between data fitting and smoothness constraint, we introduce an automatic selection scheme for a Lagrange multiplier, which is sought at each iteration with a least misfit criterion. In this selection scheme, the IE algorithm is quite attractive for saving computing time because Green's functions, whose calculation is a most time-consuming part in IE methods, are repeatedly re-usable throughout the inversion process. The inversion scheme using the LN approximation has been tested to show its stability and efficiency, using both synthetic and field data. The inverted image derived from the field data, collected in a pilot experiment of water-flood monitoring in an oil field, is successfully compared with that derived by a 2.5-dimensional inversion scheme.