• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1330-1337
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• 2004

In this study, the equations of motion of a rigid rotor supported by magnetic bearings are derived via Hamilton's principle, and transformed to a state-space form for control purpose. The optimal motion control of rotor magnetic bearing system based on the LQR(linear quadratic regulator) theory is addressed. New schemes related to the selection of the state weighting matrix Q and the control weighting matrix R involved in the quadratic functional to be minimized are proposed. And the robust control of the system with an LMI(linear matrix inequality) based H$_{\infty}$ theory is dealt with in this paper. Loop shapings of TFM (transfer function matrix) are used to increase the performance of control capability of the system. The control abilities of LQR and H$_{\infty}$ controller are compared by simulation and experimental tests and show that the capability of H$_{\infty}$ controller is superior to that of LQR.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3128-3149
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• 2018

A number of effective methods for multiple-attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy numbers (IVIFNs) have been proposed in recent years. However, the different methods frequently yield different, even sometimes contradictory, results for the same problem. In this paper a novel criterion to determine the advantages and disadvantages of different methods is proposed. First, the decision-making process is divided into three parts: translation of experts' preferences, aggregation of experts' opinions, and comparison of the alternatives. Experts' preferences aggregation is considered the core step, and the quality of the collective matrix is considered the most important evaluation index for the aggregation methods. Then, methods to calculate the similarity measure, correlation, correlation coefficient, and energy of the intuitionistic fuzzy matrices are proposed, which are employed to evaluate the collective matrix. Thus, the optimal method can be selected by comparing the collective matrices when all the methods yield different results. Finally, a novel approach for aggregating experts' preferences with IVIFN is presented. In this approach, experts' preferences are mapped as points into two-dimensional planes, with the plant growth simulation algorithm (PGSA) being employed to calculate the optimal rally points, which are inversely mapped to IVIFNs to establish the collective matrix. In the study, four different methods are used to address one example problem to illustrate the feasibility and effectiveness of the proposed approach.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.133-136
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• 1987

This paper presents a new algorithm of optimal measurement system by using band matrix characteristic respectively for state estimation. A performance index of measurement system is established to reflect relation among measurement sets, probability of measurement failure and cost of individual meter installation. Selection ranking in the candidates of measurement sets is composed to guarantee the observability for any any single meter outage. Performance index sensitivity is introduced and recursive formula which based on the matrix inversion lemma used for selection. The proposed algorithm is composed of successive addition algorithm, successive elimination algorithm and combinatorial algorithm. The band matrix characteristic could save in memory requirements and calculate the performance index faster than earlier.

• Smart Structures and Systems
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• v.9 no.3
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• pp.231-251
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• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• Proceedings of the KIEE Conference
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• 1989.11a
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• pp.407-410
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• 1989

Optimizing transient response for both tracking reference signals and disturbance rejection is determined by the poles and zeros of the transfer function. Thus, optimal pole assignment and how should weighting matrix for the performance index be chosen is very important to achieve optimum transient response. This paper focus its attention on the choosing and analysis of weighting matrix for optimum pole assignment. Optimum pole assignment is defined for linear time-invariant continuous systems.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.21-49
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• 1986

A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.11
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• pp.1048-1052
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• 2007

This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

• Journal of Astronomy and Space Sciences
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• v.25 no.3
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.

• Genomics & Informatics
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• v.1 no.1
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• pp.20-24
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• 2003

The analysis of DNA microarry data is one of the most important things for functional genomics research. The matrix representation of microarray data and its successive 'optimal' incisional hyperplanes is a useful platform for developing optimization algorithms to determine the optimal partitioning of pairwise proximity matrix representing completely connected and weighted graph. We developed Deterministic Annealing (DA) approach to determine the successive optimal binary partitioning. DA algorithm demonstrated good performance with the ability to find the 'globally optimal' binary partitions. In addition, the objects that have not been clustered at small non­zero temperature, are considered to be very sensitive to even small randomness, and can be used to estimate the reliability of the clustering.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.63-82
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• 1997

In experimental situations where n two or three level fac-tors are involoved and n observations are taken then the D-optimal first order saturated design is an $n{\times}n$ matrix with elements $\pm$1 or 0, $\pm$1, with the maximum determinant. Cononical forms are useful for the specification of the non-isomorphic D-optimal designs. In this paper we study canonical forms such as the Smith normal form the first sec-ond and the jordan canonical form of D-optimal designs. Numerical algorithms for the computation of these forms are described and some numerical examples are also given.