• Communications for Statistical Applications and Methods
• /
• 제2권2호
• /
• pp.376-386
• /
• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

• 충청수학회지
• /
• 제29권4호
• /
• pp.663-676
• /
• 2016

In this paper we propose a new family of eighth order optimal methods for solving nonlinear equations by using weight function methods. The methods of the family require three function and one derivative evaluations per step and has order of convergence eight, and so they are optimal in the sense of Kung-Traub hypothesis. Precise analysis of convergence is given. Some members of the family are compared with several existing methods to show their performance and as a result to confirm that our methods are as competitive as compared to them.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제50권11호
• /
• pp.514-521
• /
• 2001

This paper uses the distributed heating thin metal moving at constant velocity which are modeled as distributed parameter systems, and applies the Paley order of Walsh functions to high order partial differential equations and matrix partial differential equations. This thesis presents a new algorithm which usefully exercises the optimal control in the distributed parameter systems. In this paper, the excellent consequences are found without using the existing decentralized control or hierarchical control method.

• 산업경영시스템학회지
• /
• 제33권2호
• /
• pp.1-8
• /
• 2010

A vendor selection problem consists of two different kinds of decision making. First one is to choose the best suppliers among all possible suppliers and the next is to allocate the optimal quantities of orders among the selected vendors. In this study, an integration of the technique for order preference by similarity to ideal solution (TOPSIS) and a multi-objective mixed integer programming (MOMIP) is developed to account for all qualitative and quantitative factors which are used to evaluate and choose the best group of vendors and to decide the optimal order quantity for each vendor. A solution methodology for the vendor selection model of multiple-vendor, multiple-item with multiple decision criteria and in respect to finite vendor capacity is presented.

• Communications for Statistical Applications and Methods
• /
• 제26권6호
• /
• pp.527-538
• /
• 2019

This paper considers the issue of obtaining the optimal design in Poisson regression model when the sample size is small. Poisson regression model is widely used for the analysis of count data. Asymptotic theory provides the basis for making inference on the parameters in this model. However, for small size experiments, asymptotic approximations, such as unbiasedness, may not be valid. Therefore, first, we employ the second order expansion of the bias of the maximum likelihood estimator (MLE) and derive the mean square error (MSE) of MLE to measure the quality of an estimator. We then define DM-optimality criterion, which is based on a function of the MSE. This criterion is applied to obtain locally optimal designs for small size experiments. The effect of sample size on the obtained designs are shown. We also obtain locally DM-optimal designs for some special cases of the model.

• Journal of Mechanical Science and Technology
• /
• 제19권spc1호
• /
• pp.452-460
• /
• 2005

Based on an introduced optimal trajectory planning method, this paper mainly deals with the accuracy analysis during the function approximation process of the optimal trajectory planning method. The basis functions are composed of Hermit polynomials and Fourier series to improve the approximation accuracy. Since the approximation accuracy is affected by the given orders of each basis function, the accuracy of the optimal solution is examined by changing the combinations of the orders of Hermit polynomials and Fourier series as the approximation basis functions. As a result, it is found that the proper approximation basis functions are the $5^{th}$ order Hermit polynomials and the $7^{th}-10^{th}$ order of Fourier series.

• Journal of Advanced Marine Engineering and Technology
• /
• 제6권2호
• /
• pp.42-50
• /
• 1982

The controller, generally, is to be designed to optimize the system in somesence subject to some constraints. In this paper the method to determine the optimal parameters of the PI controller in the unity feed back control system is proposed. Here the sence of the optimal is to minimize the integral of the squared error under the constraints that the maximum absolute value of control input, maximum overshoot, rise time, etc., should be smaller than the pre-given values. In the analysis the traditional method and the state variable method are combined in order to reduce the computational procedures required in the design of PI controller. Therefore, the procedure proposed in the paper is usefully applicable to the controller system with a general second-order plant. Finally, the indicial response curves generated at the optimal state are compared with those of non-optimal state and the effectiveness of this method is assertained.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
• /
• pp.388-388
• /
• 2000

The complexity of nonlinear systems makes it difficult to ascertain their behavior using classical methods of analysis. Many efforts have been focused on the advanced algorithms and techniques that hold the promise of improving real-time optimal control while at the same time providing higher accuracy. In this paper, a fuzzy cell mapping method of real-time optimal control far nonlinear dynamical systems is proposed. This approach combines fuzzy logic with cell mapping techniques in order to find the optimal input level and optimal time interval in the finite set which change the state of a system to achieve a desired obiective. In order to illustrate this method, we analyze the behavior of an inverted pendulum using fuzzy cell mapping.

• 대한수학회지
• /
• 제46권5호
• /
• pp.1007-1025
• /
• 2009

First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $H^{-1}$ and $L^2$ norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

• Journal of applied mathematics & informatics
• /
• 제40권5_6호
• /
• pp.857-871
• /
• 2022

In this work, we formulated a mathematical model for divorce in marriage and extended in to an optimal control model. Firstly, we qualitatively established the model positivity and boundedness. Also we saw sensitivity analysis of the model and identified the positive and negative indices parameters. An optimal control model were developed by incorporating three time dependent control strategies (couple relationship education, reducing getting married too young & consulting separators to renew their marriage) on the deterministic model. The Pontryagin's maximum principle were used for the derivation of necessary conditions of the optimal control problem. Finally, with Newton's forward and backward sweep method numerical simulation were performed on optimality system by considering four integrated strategies. So that we reached to a result that using all three strategies simultaneously (the strategy D) is an optimal control in order to effectively control marriage divorce over a specified period of time. From this we conclude that, policymakers and stakeholders should use the indicated control strategy at a time in order to fight against Divorce in a population.