• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1069-1096
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• 2015

In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.4
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• pp.371-379
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• 1990

The decoupling problem has a great practical importance in that it simplifies greatly the control of a given system by reducing the multi-input multi-output systems. In this paper, we derive the necessary and sufficient conditions for decoupling 2-D F-MM II via state feedback. For the general case, the problem of determining the feedback matrix F involves the solution of nonlinear algebraic equations. Under certain conditions, however, it is shown that an explicit formula for F may be derived. In comparsion with the method for FM, it appears that this method for F-MM II is more general and the algorithm is simpler.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.81-84
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• 1996

We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.781-784
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• 1998

An image segmentation approach based on the fuzzy worm searching and MIN-MAx clusterng algorithm is proposed in this paper. This algorithm deals with fuzzy worm value and min-max node at a gross scene level, which investigates the edge information including fuzzy worm action. But current segmentation methods based edge extraction methods generally need the mask information for the algebraic model, and take long run times at mask operation, wheras the proposed algorithm has single operation ccording to active searching of fuzzy worms. In addition, we also genetic min-max clustering using genetic algorithm to complete clustering and fuzyz searching on grey-histogram of image for the optimum solution, which can automatically determine the size of rnages and has both strong robust and speedy calculation. The simulation results showed that the proposed algorithm adaptively divided the quantized images in histogram region and performed single searching methods, significantly alleviating the increase of the computational load and the memory requirements.

• International Journal of Control, Automation, and Systems
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• v.1 no.2
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• pp.171-177
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• 2003

In this paper, we investigate a robust $H_{\infty}$ state feedback control technique for continuous time bilinear systems with an additive disturbance input. The nonlinear robust $H_{\infty}$control for bilinear systems requires a solution to the state dependent algebraic Riccati equation (SDARE). We present a new robust $H_{\infty}$control technique based on the successive approximation method for solving the SDARE by converting bilinear systems into time-varying linear systems. The proposed control method guarantees robust stability for closed loop bilinear systems. The proposed algorithm is verified by numerical examples.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.159-167
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• 2000

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

• Proceedings of the KSR Conference
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• 2001.10a
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• pp.329-334
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• 2001

This paper presents exact autotransformer-fed AC electric railroad system modeling using constant current mode. The theory is based on the solution of algebraic. The proposed modeling is considered the line self-impedances and mutual-impedances. Besides, the load modeling improved results are obtained as application to the proposed constant current mode. In the analysis on AT-fed AC electric railroad system circuit, a generalized analysis method using the loop equation on a case by case. the simulation objectives are to calculate the catenary and rail voltages with respect to ground, as the train moves along a section of line between two adjacent ATs. The model contains assumptions regarding the representation of the autotransformer, the impedance of the track/catenary system, and the grounding arrangements, which all effect the accuracy of the result. The modeling results seem very reasonable. It is established that techniques for the AC electric railroad system modeling and analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.125-136
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• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.356-368
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• 1992

The strongly interactive flow field near a missile afterbody containing a centered exhaust jet is numerically investigated. The thin shear layer and full formulation of compressible, Reynolds I averaged Navier-Stokes equations are solved. A time-dependent implicit numericals algorithm is used to obtain solution for a variety of flow conditions. Turbulence closure is implemented by the Baldwin-Lomax algebraic eddy viscosity model. An adaptive grid technique is adopted to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computation, Numerical results show good agreemement with experimental data in all regimes.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1800-1805
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• 2008

A "finite volume method" is proposed to predict heat transport in a spherical enclosure at micro/nanoscale with the Boltzmann transport equation (BTE). The gray version of the BTE with the relaxation time approximation has been applied. Pointing out similarity between radiative transfer equation (RTE) and BTE, the mapping process in RTE is adopted to treat the angular derivative term and linear algebraic discretization equation is derived by using the established method which is used in 2-D BTE in cartesian coordinates. The simulation results are compared to exact solution to RTE for various acoustic thicknesses and ratio of radii. The comparison shows that this method is logical and accurate, and it is possible to easily adopt various models in spherical BTE.