• Journal of Institute of Control, Robotics and Systems
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• v.18 no.3
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• pp.175-180
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• 2012

A nonlinear navigation filter for biomimetic robot using analytic approximation of mean and covariance of state variable is proposed. The approximations are performed at the time update step in the filter structure. The mean is approximated to the 3rd order of Taylor's series expansion of true mean and the covariance is approximated to the 3rd order either. The famous EKF is a nonlinear filtering method approximating the mean to 1st order and the covariance to the 3rd order. The UKF approximate them to the higher orders by numerical method. The proposed method derived a analytical approximation of them for navigation system and therefore don't need so called sigma point transformation in UKF. The simulation results show that the proposed method can be a good alternative of UKF in the systems which require less computational burden.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.4
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• pp.583-589
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• 1987

A new approximation method is proposed for the linear model reduction of high order dynamic systems. This mehtod is based upon the denominator table(D-table) and time moment-matching technique. The denominator table(D-table) is used to obtain the denominator polynomial of reduced-order model, and the numerator polynomial is obtained by time moment-matching method. This proposed method does not require the calculation of the alpha-beta expansion and reciprocal transformation which should be calculadted by Routh approximation method. The advantages of the proposed method are that it is computationally every attractive better than Routh approximation method and the reduced model is stable Il the original system is stable.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.467-484
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• 2022

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1041-1049
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• 2003

In this paper, a new local two-point approximation method which is based on the exponential intervening variable is proposed. This new algorithm, called the Two-Point Convex Approximation(TPCA), use the function and design sensitivity information from the current and previous design points of the sequential approximate optimization to generate a sequence of convex, separable subproblems. This paper describes the derivation of the parameters associated with the approximation and the numerical solution procedure. In order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve several typical design problems. These optimization results are compared with those of other optimizers. Numerical results obtained from the test examples demonstrate the effectiveness of the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.171-179
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• 2013

In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.660-669
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• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.935-942
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• 2001

A finite element approximation of a fourth-order nonlinear boundary value problem is given. In the direct implementation, a nonlinear system will be obtained and also a full size matrix will be introduced when Newton’s method is adopted to solve the system. To avoid this difficulty we introduce an iterative scheme which can be shown to converge the positive solution of the system lying between 0 and $sin{\pi}x$.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.12
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• pp.209-219
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• 1995

As a new algorithm for RC tree delay estimation, we propose a $\tau$-model of the driver and a moment propagation method. The $\tau$-model represents the driver as a Thevenin equivalent circuit which has a one-time-constant voltage source and a linear resistor. The new driver model estimates the input voltage waveform applied to the RC more accurately than the k-factor model or the 2-piece waveform model. Compared with Elmore method, which is a lst-order approximation, the moment propagation method, which uses $\pi$-model loads to calculate the moments of the voltage waveform on each node of RC trees, gives more accurate results by performing higher-order approximations with the same simple tree walking algorithm. In addition, for the instability problem which is common to all the approximation methods using the moment matching technique, we propose a heuristic method which guarantees a stable and accureate 2nd order approximation. The proposed driver model and the moment propagation method give an accureacy close to SPICE results and more than 1000 times speedup over circuit level simulations for RC trees and FPGA interconnects in which the interconnect delay is dominant.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.10a
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• pp.419-424
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• 1999

In this paper, the comparison of the first order approximation schemes such as SLP (sequential linear programming), CONLIN(convex linearization), MMA(method of moving asymptotes) and the second order approximation scheme, SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP are the most efficient methods for optimization. But the number of function call of SQP is much more than that of MMA. Therefore, when it is considered with the expense of computation, MMA is more efficient than SQP. In order to examine the efficiency of MMA for complex optimization problem, it was applied to the helicopter tail boom considering column buckling and local wall buckling constraints. It is concluded that MMA can be a very efficient approximation scheme from simple problems to complex problems.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.8-12
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• 2004

In this study we consider a CONWIP system in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied are backordered according to the number of demands that exist at their arrival instants. For this system we develop an approximation method to calculate order based performance measures such as the mean time of fulfilling a customer order and the mean number o: customer orders. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interest.