• Title/Summary/Keyword: Matrix function

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Robust Multiloop Controller Design of Uncertain Affine TFM(Transfer Function Matrix) System (불확실한 Affine TFM(Transfer Function Matrix) 시스템의 강인한 다중 루프 제어기 설계)

  • Byun Hwang-Woo;Yang Hai-Won
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.54 no.1
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    • pp.17-25
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    • 2005
  • This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.

The Study of Adjusting the Cost Matrix in Loss Function Approach for Multiresponse Optimization (다중 반응 변수 문제 해결을 위한 손실 함수 방법에서 비용 행렬의 보정에 관한 연구)

  • Lee Dae-Won;Kim So-Hui;Kim Gwang-Jae;Lee Jae-Uk
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2004.10a
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    • pp.31-34
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    • 2004
  • For solving multiresponse problems, a variety of loss function approaches have been proposed assuming that a cost matrix is known and fixed. However a cost matrix is also an important factor in loss function approaches, because the optimal solution is very sensitive to the cost matrix. In this paper. we propose a novel method for adjusting the cost matrix by considering the predictive ability of the estimated response models. Simulation results for the generated data set show that the proposed method is competitive with previously reported methods.

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SMOOTH SINGULAR VALUE THRESHOLDING ALGORITHM FOR LOW-RANK MATRIX COMPLETION PROBLEM

  • Geunseop Lee
    • Journal of the Korean Mathematical Society
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    • v.61 no.3
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    • pp.427-444
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    • 2024
  • The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Typical approaches to matrix completion problem often rely on thresholding the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain more accurate and robust estimation of the data matrix. Furthermore, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results demonstrate that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

Relaxed Stability Condition for Affine Fuzzy System Using Fuzzy Lyapunov Function (퍼지 리아푸노프 함수를 이용한 어파인 퍼지 시스템의 완화된 안정도 조건)

  • Kim, Dae-Young;Park, Jin-Bae;Joo, Young-Hoon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.61 no.10
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    • pp.1508-1512
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    • 2012
  • This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

SZEGÖ PROJECTIONS FOR HARDY SPACES IN QUATERNIONIC CLIFFORD ANALYSIS

  • He, Fuli;Huang, Song;Ku, Min
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.1215-1235
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    • 2022
  • In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

Identification of Damping Matrix for a Steel Bar by the Genetic Algorithm (유전알고리즘에 의한 강봉의 감쇠행렬 산출법)

  • Park, Sok-Chu;Park, Young-Bum;Park, Kyoung-Il;Je, Hye-Kwang;Yi, Geum-Joo
    • Journal of Advanced Marine Engineering and Technology
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    • v.35 no.2
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    • pp.271-277
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    • 2011
  • An identification method of the structural damping matrix for a steel bar by the genetic algorithm is proposed. Supposing the damping matrix were in proportion to the stiffness matrix, the proportional factors can be identified from the curve fitting of the experimental frequency response function(FRF) by the genetic algorithm. Applying the identified damping matrix to FEM of a beam model, the values of the objective function could be reduced to about 1/60 in comparison with conventional FEM model without damping. The damping matrices of some sub-structures which have large damping partly could be identified by the algorithm, and they could be used as some parts of the FEM model for a whole structure.

THE BASIC KONHAUSER MATRIX POLYNOMIALS

  • Shehata, Ayman
    • Honam Mathematical Journal
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    • v.42 no.3
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    • pp.425-447
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    • 2020
  • The family of q-Konhauser matrix polynomials have been extended to Konhauser matrix polynomials. The purpose of the present work is to show that an extension of the explicit forms, generating matrix functions, matrix recurrence relations and Rodrigues-type formula for these matrix polynomials are given, our desired results have been established and their applications are presented.

Process Methology of Designing User Interface in Enterprise Portal (기업포탈사이트 업무화면 설계 프로세스 방법론 - 보험사의 프로젝트 진행 사례를 중심으로)

  • Kwon, Suk-Kyoung
    • 한국HCI학회:학술대회논문집
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    • 2008.02b
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    • pp.310-316
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    • 2008
  • This theory focuses on the Enterprise Portal and researches and analyzes the user requirement on as-is system. The UI Checklist Matrix is made based on the result of user analysis and evaluation of checklist. The horizontal axis of the Matrix is composed of 6 results(Layout, Navigation, Information, Function, Visibility and Interaction) of user requirement analysis. The vertical axis of the Matrix is composed of 10 subjects, Learnability, Efficiency, Accuracy, Accessibility, Consistency, Agility, Convergence, Personalization, Technology, and Standardization. At the point of vertical and horizontal items meet, indicates the graded of importance and defines a details item. The Guideline in which Matrix is reflected is set and according to the guideline, designing the business screen and assessing the Matrix.

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System Requirement Analysis of Multi-Role Helicopter by Implementing Quality Function Deployment (QFD(Quality Function Deployment)를 이용한 다목적 헬리콥터의 시스템 요구도 분석)

  • Kim, Minji;Park, Mi-Young;Lee, Jae-Woo;Byun, Younghan
    • Journal of the Korean Society of Systems Engineering
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    • v.1 no.2
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    • pp.56-62
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    • 2005
  • In this study, we first define user requirements to fulfill the reconnaissance and the search missions, by analyzing the system characteristics and operation environment. By investigating the design technology level, the development and procurement costs, the strong system design concepts and possible alternatives will be proposed. To analyze the system requirements, the Quality Function Deployment of the systems engineering approach will be implemented. The promising design alternatives that satisfy the user requirements are extracted by constructing the Morphological Matrix, then the best design concept will be obtained using the Pugh Concept Selection Matrix and the TOPSIS(Technique of Order Preference by Similarity to Ideal Solution).

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UNDERSTANDING NON-NEGATIVE MATRIX FACTORIZATION IN THE FRAMEWORK OF BREGMAN DIVERGENCE

  • KIM, KYUNGSUP
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.25 no.3
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    • pp.107-116
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    • 2021
  • We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.