• Korean Journal of Mathematics
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• v.6 no.1
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• pp.27-46
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• 1998

We are concerned with an optimal control problem governed by a Poisson equation in which body force acts like a control parameter. The cost functional to be optimized is taken to represent the error from the desired observation and the cost due to the control. We recast the problem into the mixed formulation to take advantage of the minimax principle for the duality method. The existence of a saddle point for the Lagrangian shall be shown and the optimality system will be derived therein. Finally, to attain an optimal control, we combine the optimality system with an operational technique. By achieving the gradient of the cost functional, a convergent algorithm based on the projected gradient method is established.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.263-266
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• 1996

A method to determine an optimal temperature trajectory that guarantees polymer products having controlled molecular weight distribution and desired values of molecular weight is presented. The coordinate transformation method and the optimal control theory are applied to a batch PMMA polymerization system to calculate the optimal temperature trajectory. Coordinate transformation method converts the original fixed-end-point, free-end-time problem to a free-end-point, fixed-end-time problem. The idea is that by making the reactor temperature track the optimal temperature trajectory one may be able to produce polymer products having the prespecified physical property in a minimum time. The on-line control experiments with the PID control algorithm have been conducted to establish the validity of the scheme proposed in this study. The experimental results show that prespecified polymer product could be obtained with tracking the calculated optimal temperature trajectory.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.19-30
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• 2013

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.28-33
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• 1994

An optimal controller, e.g. LQG controller, may not be realistic in the sense that the required control power may not be achieved by existing actuators, and the measured output is not satisfactory. To be realistic, the controller should meet such constraints as sensor or actuator limitation, performance limit, etc. In this paper, the lnput/Output Variance Constrained (IOVC) control problem will be considered from the viewpoint of mathematical programming. A dual version shall be developed to solve the IOVC control problem, whose objective is to find a stabilizing control law attaining a minimum value of a quadratic cost function subject to the inequality constraint on each input and output variance for a stabilizable and detectable plant. One approach to the constrained optimization problem is to use the Kuhn-Tucker necessary conditions for the optimality and to seek an optimal point by an iterative algorithm. However, since the algorithm uses only the necessary conditions, the convergent point may not be optimal solution. Our algorithm will guarantee a sufficiency.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.578-583
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• 1992

In this paper, we show that various navigation constant values in PNG law can result in as optimal gains when we introduce proper time-varying weighting functions into the cost function of an optimal control problem. we then apply this idea to the guidance problem where we are required to achieve a given impact angle as well as the zero miss distance. As a result, we obtain a set of optimal guidance laws each of which could be related to a navigation constant in PNG. Some basic properties of these guidance laws are also presented.

• East Asian mathematical journal
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• v.35 no.5
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• pp.547-557
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• 2019

This paper is concerned with the necessary conditions for optimal control problem governed by some ODE-PDE systems. That is, we obtain the necessary conditions for optimal control by showing the differentiability of the solution with respect to the control.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.421-424
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• 1987

Recently, the problem associated with the achievement of desired trajectories for non-linear robotic manipulatory systems are researched. The control system which is designed for this robot manipulator, poses a number of severe problem. The methods proposed to deal with the problem fall loosely into three main classes : "direct" "adaptive", "anthropomorphic". Besides there is an approach which is described based upon the application of optimal control theory. In this paper, using the optimal theory, we choose error-coordinate, between the desired trajectories and the practical as the state values, and determine the control law U which minimize a corresponding performance criterion. Let's consider the robotic arm proposed by Freund and set up the deviations of it's trajectory as a measure of performance. To find the optimal control law $U^*$ and the next state value which need to obtain $U^*$ here, we should introduced the conjugate gradient algorithm and the Runge Kutta method.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.432-435
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• 1995

In this paper a new approach to obtain the solution of the linear-quadratic Gaussian control problem for singularly perturbed discrete-time stochastic systems is proposed. The alogorithm proposed is based on exploring the previous results that the exact solution of the global discrete algebraic Riccati equations is found in terms of the reduced-order pure-slow and pure-fast nonsymmetric continuous-time algebraic Riccati equations and, in addition, the optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.

• East Asian mathematical journal
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• v.34 no.5
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• pp.683-691
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• 2018

We consider an optimal control problem for an impulsive stage-structured model involving ordinary differential equations with impulsive values of initial conditions in the next year. The main goal is to maximize a profit of the catch of Pacific cod in the South Korea through optimal harvest strategy as a control of adult cod. We established necessary conditions for the optimal harvest control using idea of Pontryagin's maximum principle. The optimal harvest strategy is to numerically solve the equation by using an iterative method with the Runge-Kutta method. Finally, we compare a monthly average of fishing mortality of Pacific cod from 2013 to 2017 with monthly fishing mortality for result obtained optimal harvest strategy.