• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권2호
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• pp.77-105
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• 2014

Medical imaging techniques have evolved to expand our ability to visualize new contrast information of electrical, optical, and mechanical properties of tissues in the human body using noninvasive measurement methods. In particular, electrical tissue property imaging techniques have received considerable attention for the last few decades since electrical properties of biological tissues and organs change with their physiological functions and pathological states. We can express the electrical tissue properties as the frequency-dependent admittivity, which can be measured in a macroscopic scale by assessing the relation between the time-harmonic electric field and current density. The main issue is to reconstruct spectroscopic admittivity images from 10 Hz to 1 MHz, for example, with reasonably high spatial and temporal resolutions. It requires a solution of a nonlinear inverse problem involving Maxwell's equations. To solve the inverse problem with practical significance, we need deep knowledge on its mathematical formulation of underlying physical phenomena, implementation of image reconstruction algorithms, and practical limitations associated with the measurement sensitivity, specificity, noise, and data acquisition time. This paper discusses a number of issues in electrical tissue property imaging modalities and their future directions.

• 제어로봇시스템학회논문지
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• 제9권1호
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• pp.50-56
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• 2003

In electrical impedance tomography(EIT), various image reconstruction algorithms have been used in order to compute the internal resistivity distribution of the unknown object with its electric potential data at the boundary. Mathematically the EIT image reconstruction algorithm is a nonlinear ill-posed inverse problem. This paper presents a new combined method based on genetic algorithm(GA) and modified Newton-Raphson(mNR) algorithm via two-step approach for the solution of the static EIT inverse problem. In the first step, each mesh is classified into three mesh groups: target, background, and temporary groups. The mNR algorithm can be used to determine the region of group. In the second step, the values of these resistivities are determined using genetic algorithm. Computer simulations with the 32 channels synthetic data show that the spatial resolution of reconstructed images by the proposed scheme is improved compared to that of the mNR algorithm at the expense of increased computational burden.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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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.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.53-66
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• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2002년도 합동 추계학술대회 논문집 정보 및 제어부문
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• pp.513-516
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• 2002

In electrical impedance tomography(EIT), various image reconstruction algorithms have been used in order to compute the internal resistivity distribution of the unknown object with its electric potential data at the boundary. Mathematically the EIT image reconstruction algorithm is a nonlinear ill-posed inverse problem. This paper presents two intelligent optimization algorithm techniques such as genetic algorithm and simulated annealing for the solution of the static EIT inverse problem. We summarize the simulation results for the three algorithm forms: modified Newton-Raphson, genetic algorithm, and simulated annealing.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 가을 학술발표회 논문집
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• pp.262-269
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• 1997

The purpose of this study is to survey the shape finding of the plane truss structures under the prescribed displacement mode by the shape analysis. The shape analysis is peformed by the existence condition of a solution and Moore-Penrose generalized inverse matrix, and the prescribed displacement mode is the homologous deformation of structures. The shape analysis of structures is a kind of inverse problem and become the problem of a nonlinear equation. Newton-Raphson method is used to improve the accuracy of approximated solution. To prove the accuracy and the effectiveness of this method, four different shape examples are analyzed.

• Structural Engineering and Mechanics
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• 제12권5호
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• pp.527-540
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• 2001

A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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• pp.93-98
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• 2001

This paper studies on the design of an ILQ(Inverse Linear Quadratic optimal control) looper control system for hot strip mills. The looper which is placed between each stand plays an important role in controlling strip width by regulating strip tension variation generated from the velocity difference of main work rolls. The mathematical model for looper is firstly obtained by Taylor's linearization of nonlinear differential equations, where it is given as a linear and time invariant state-space equation. Secondly, a looper servo controller is designed by ILQ control algorithm, which is an inverse problem of LQ(Linear Quadratic optimal control) control. By tunning control gain arbitration parameters and time constants, it is shown that the ILQ looper servo controller has the performance that makes well to follow desired trajectories of both strip tension and looper angle.

• International Journal of Control, Automation, and Systems
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• 제6권3호
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• pp.364-377
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• 2008

Due to the difficulty in solving the Hamilton-Jacobi-Isaacs equation, the nonlinear optimal control approach is not very practical in general. To overcome this problem, Ezal et al. (2000) first solved a linear optimal control problem for the linearized model of a nonlinear system given in the strict-feedback form. Then, using the backstepping procedure, a nonlinear feedback controller was designed where the linear part is same as the linear feedback obtained from the linear optimal control design. However, their construction is based on the cancellation of the high order nonlinearity, which limits the application to the smooth ($C^{\infty}$) vector fields. In this paper, we develop an alternative method for backstepping procedure, so that the vector field can be just $C^1$, which allows this approach to be applicable to much larger class of nonlinear systems.

• 대한수학회지
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• 제55권4호
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.