• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.601-606
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• 1999

A Walsh function method is proposed in this report for the analysis and optimal control of linear time-delay systems, which is based on the Picard's iterative approximation and fast Walsh transformation. In this research, the following results are obtained: 1) The differential and integral equation can be solved by transforming into a simple algebraic equation as it was possible with the usual orthogonal function method: 2) General orthogonal function methods require usage of Walsh operational matrices for delay or advance and many calculations of inverse matrices, which are not necessary in this method. Thus, the control problems of linear time-delay systems can be solved much faster and readily.

• The Mathematical Education
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• v.62 no.2
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• pp.269-287
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• 2023

Matrix theory is widely used not only in mathematics, natural sciences, and engineering, but also in social sciences and artificial intelligence. In the 2009 revised mathematics curriculum, matrices were removed from high school math education to reduce the burden on students, but in anticipation of the age of artificial intelligence, they will be reintegrated into the 2022 revised education curriculum. Therefore, there is a need to analyze the matrix content covered in other countries to suggest a meaningful direction for matrix education and to derive implications for textbook composition. In this study, we analyzed the German mathematics curriculum and standard education curriculum, as well as the matrix units in the German Hesse state mathematics curriculum and textbook, and identified the characteristics of their content elements and development methods. As a result of our analysis, it was found that the German textbooks cover matrices in three categories: matrices for solving linear equations, matrices for explaining linear transformations, and matrices for explaining transition processes. It was also found that the emphasis was on mathematical reasoning and modeling when learning matrices. Based on these findings, we suggest that if matrices are to be reintegrated into school mathematics, the curriculum should focus on deep conceptual understanding, mathematical reasoning, and mathematical modeling in textbook composition.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.373-385
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• 2007

The solution of the normal equation arising in a general linear model by the least square methods is not unique in general. Conventionally, SAS IML and G-inverse matrices are considered for such problems. In this paper, we provide a systematic solution procedures for SAS IML.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.443-445
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• 1998

In this paper, an alternate method for state-covariance assignment for SISO(single input single output) linear systems is proposed. This method is based on the inverse solution of the Lyapunov matrix equation and the resulting formulas are similar in structure to the formulas for pole placement. Further, the set of all assignable covariance matrices to a SISO linear system is also characterized.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.969-990
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• 2011

Assume that X, partitioned into $2{\times}2$ block form, is a solution of the system of quaternion matrix equations $A_1XB_1$ = $C_1,A_2XB_2=C_2$. We in this paper give the maximal and minimal ranks of the submatrices in X, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. As applications, we consider the common inner inverse G, partitioned into $2{\times}2$ block form, of two quaternion matrices M and N. We present the formulas of the maximal and minimal ranks of the submatrices of G, and describe the properties of the submatrices of G as well. The findings of this paper generalize some known results in the literature.

• Journal of Mechanical Science and Technology
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• v.18 no.5
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• pp.780-788
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• 2004

To avoid the unit inconsistency problem in the conventional Jacobian matrix, new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points was presented (Kim and Ryu, 2003). This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived unit consistent Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.

• Journal of Korean Association for Spatial Structures
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• v.3 no.2 s.8
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• pp.101-107
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• 2003

There exists a structural problem for link structures in the unstable state. The primary characteristics of this problem are in the existence of rigid body displacements without strain, and in the possibility of the introduction of prestressing to change an unstable state into a stable state. When we make local linearized incremental equations in order to obtain knowledge about these unstable structures, the determinant of the coefficient matrices is zero, so that we face a numerically unstable situation. This is similar to the situation in the stability problem. To avoid such a difficult situation, in this paper a simple and straightforward method was presented by means of the generalized inverse for the numerical analysis of stability problem.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.140-145
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• 2001

Various control algorithms are available to suppress the vibration of a system subjected to disturbances. LQ algorithm is simple and easy to implement the hardwares, but it lacks robustness for uncertainties and often causes difficulty in determining the weighting matrices. This study focuses on the effectiveness ILQ(Inverse Linear Quadratic optimal control) algorithm as the alternative to LQ applied to control the vibration of a building under the seismic excitation. The building is of moment resisting steel frames and assumed to behave within the elastic range. The brief overview of LQ and ILQ algorithms is introduced, and the displacement responses of the structure using ILQ algorithm are compared with those obtained from LQ control. The magnitude of control forces are also determined and compared for both LQ and ILQ algorithm.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.529-531
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• 2001

We present an expectation-maximization algorithm for principal component analysis via orthogonalization. The algorithm finds actual principal components, whereas previously proposed EM algorithms can only find principal subspace. New algorithm is simple and more efficient thant probabilistic PCA specially in noiseless cases. Conventional PCA needs computation of inverse of the covariance matrices, which makes the algorithm prohibitively expensive when the dimensions of data space is large. This EM algorithm is very powerful for high dimensional data when only a few principal components are needed.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.54.1-54
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• 2001

In this paper, an alternate method for state-covariance assignment for SISO(single input singe output) linear systems is proposed. This method is based on the inverse solution of the Lyapunov matrix equation and the resulting formulas are similar in structure to the formulas for pole placement. Further, the set of all assignable covariance matrices to a SISO linear system is also characterized.