• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.97-113
• /
• 2004

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1993.04a
• /
• pp.135-140
• /
• 1993

The optimum weight design of structure is to determine the combination of structural members which minimize the weight of structures and satisfy design conditions as well. Since most of loads and design variables considered in structural design have uncertain natures, the reliability-based optimization techniques need to be developed. The aim of this study is to estabilish the general algorithm for the minimum weight design of transmission tower structure system with reliability constraints. The sequential linear programming method is used to solve non-linear minimization problems, which converts original non-linear programming problems to sequential linear programming problems. The optimal solutions are produced for various reliability levels such as reliability levels inherent in current standard transmission tower cross-section and optimal transmission tower cross-section obtained with constraints of current design criteria as well as selected target reliability index. The optimal transmission towers satisfying reliability constraints sustain consistent reliability levels on all members. Consequently, more balanced optimum designs are accomplished with less structural weight than traditional designs dealing with deterministic design criteria.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.717-730
• /
• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.27.4-27
• /
• 2001

A stabilizing control method for linear systems with model uncertainties and hard input constraints is developed, which does not require on-line optimizations. This work is motivated by the constrained robust MPC(CRMPC) approach [3] which adopts the dual mode prediction strategy (i.e. free control moves and invariant set) and minimizes a worst case performance criterion. Based on the observation that, a feasible control sequence for a particular state can be found as a linear combination of feasible sequences for other states, we suggest a stabilizing control algorithm providing sub-optimal and feasible control sequences using pre-computed optimal sequences for some canonical states. The on-line computation of the proposed method reduces to simple matrix multiplication.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.20-20
• /
• 2000

Back-propagation neural network (BPNN) is the most prevalently used paradigm in modeling semiconductor manufacturing processes, which as a neuron activation function typically employs a bipolar or unipolar sigmoid function in either hidden and output layers. In this study, applicability of another linear function as a neuron activation function is investigated. The linear function was operated in combination with other sigmoid functions. Comparison revealed that a particular combination, the bipolar sigmoid function in hidden layer and the linear function in output layer, is found to be the best combination that yields the highest prediction accuracy. For BPNN with this combination, predictive performance once again optimized by incrementally adjusting the gradients respective to each function. A total of 121 combinations of gradients were examined and out of them one optimal set was determined. Predictive performance of the corresponding model were compared to non-optimized, revealing that optimized models are more accurate over non-optimized counterparts by an improvement of more than 30%. This demonstrates that the proposed gradient-optimized teaming for BPNN with a linear function in output layer is an effective means to construct plasma models. The plasma modeled is a hemispherical inductively coupled plasma, which was characterized by a 24 full factorial design. To validate models, another eight experiments were conducted. process variables that were varied in the design include source polver, pressure, position of chuck holder and chroline flow rate. Plasma attributes measured using Langmuir probe are electron density, electron temperature, and plasma potential.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.31 no.7
• /
• pp.18-24
• /
• 1982

We derived an optimal control of the Stochastic Bilinear Systems. For that we, firstly, formulated stochastic bilinear system and estimated its state when the system state is not directly observable. Optimal control problem of this system is reviewed on the line of three optimization techniques. An optimal control is derived using Hamilton-Jacobi-Bellman equation via dynamic programming method. It consists of combination of linear and quadratic form in the state. This negative feedback control, also, makes the system stable as far as value function is chosen to be a Lyapunov function. Several other properties of this control are discussed.

• International Journal of Control, Automation, and Systems
• /
• v.4 no.4
• /
• pp.456-465
• /
• 2006

The problem of recursive filtering far linear discrete-time systems with uncertainties is considered. A new suboptimal filtering algorithm is herein proposed. It is based on the fusion formula, which represents an optimal mean-square linear combination of local Kalman estimates with weights depending on cross-covariances between local filtering errors. In contrast to the optimal weights, the suboptimal weights do not depend on current measurements, and thus the proposed algorithm can easily be implemented in real-time. High accuracy and efficiency of the suboptimal filtering algorithm are demonstrated on the following examples: damper harmonic oscillator motion and vehicle motion constrained to a plane.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.183-193
• /
• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• Journal of KIISE:Software and Applications
• /
• v.34 no.3
• /
• pp.266-274
• /
• 2007

This paper proposes a new reconstruction method of high-resolution facial image from a low-resolution facial image based on top-down machine learning and recursive error back-projection. A face is represented by a linear combination of prototypes of shape and that of texture. With the shape and texture information of each pixel in a given low-resolution facial image, we can estimate optimal coefficients for a linear combination of prototypes of shape and those that of texture by solving least square minimizations. Then high-resolution facial image can be obtained by using the optimal coefficients for linear combination of the high-resolution prototypes. In addition, a recursive error back-projection procedure is applied to improve the reconstruction accuracy of high-resolution facial image. The encouraging results of the proposed method show that our method can be used to improve the performance of the face recognition by applying our method to reconstruct high-resolution facial images from low-resolution images captured at a distance.

• Proceedings of the KIEE Conference
• /
• 2000.07a
• /
• pp.347-349
• /
• 2000

Under an open transmission access, the generation dispatch is determined by the bidding process of market participants. Congestion occurs when the dispatch would result in the violation of operational constraints. Congestion problem is formulated and solved by OPF(optimal power flow) calculation. The objective functions in OPF are given as quadratic cost functions or piecewise linear functions of bidding functions. In this study, the optimization technique of generation dispatch is presented for the combination of two types of quadratic and linear cost functions.