• 전기의세계
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• v.21 no.3
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• pp.31-40
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• 1972

This study intends to investigate the optimal switching modes of a double-capacitive thermal system under different constraints on the state and the control variable, by the application of the Pontryagin's Minimum Principle. Throughout the development, the control effort is assumed to have two modes of state: M or zero and the terminal times being fixed. In the first part of this study, the Principle is discussed under various conditions for this particular problem, with different criterion functions and in the same time imposing a certain constraints; i) on the terminal states, ii) on functions of the terminal states. Depending upon the upper bound value of the control vector, possible driving modes of the states are studied from which particular optimal driving modes are extracted so as to meet the specified constraints and boundary conditions imposed in the problem. Numerical solutions are evaluated for an over0damped, double-capacitive thermal plant and the optimal solutions: the switching mode, the optimal switching time, and the control effort are compared with the analytical results, in the second part of this work, to confirm the development.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.857-871
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• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.10a
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• pp.213-216
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• 2005

In this research, we explore how to manage the transition of technology generations considering incremental innovation of the existing technology generation. Firms can slow down decaying of the existing technology by continuous incremental improvements rather than introducing a new generation technology at the first time if the former strategy is better. We characterize optimal technology transition problem by setting up an optimal control model. The model which is originally designed and solved by Thompson(1968) as a ‘Machine maintenance problem’ has been cited to build the main body of our model. With this analytical model, we derive optimal ‘incremental innovation’ strategy which is considering transition to the next technology. Our analysis indicates that there exists an unique ‘stopping incremental innovation timing’. Before the point of time, the decision maker should make his effort at a maximum level to enhance the current technology. However from the stopping timing to the final time horizon where the new technology is introduced, it is found that not to invest to the current technology any more is optimal.

• International Journal of Control, Automation, and Systems
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• v.4 no.5
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• pp.653-659
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• 2006

The design of $H_2$-optimal control with regional pole assignment via state feedback in linear time-invariant systems is investigated. The aim is to find a state feedback controller such that the closed-loop system has the desired eigenvalues lying in some desired stable regions and attenuates the disturbance between the output vector and the disturbance vector. Based on a proposed result of parametric eigenstructure assignment via state feedback in linear systems, the considered $H_2$-optimal control problem is changed into a minimization problem with certain constraints, and a simple and effective algorithm is proposed for this considered problem. A numerical example and its simulation results show the simplicity and effectiveness of this proposed algorithm.

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

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2617-2622
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• 2003

The pH neutralization process has long been taken as a representative benchmark problem of nonlinear chemical process control due to its nonlinearity and time-varying nature. For general nonlinear processes, it is difficult to control with a linear model-based control method so nonlinear controls must be considered. Among the numerous approaches suggested, the most rigorous approach is the dynamic optimization. However, as the size of the problem grows, the dynamic programming approach is suffered from the curse of dimensionality. In order to avoid this problem, the Neuro-Dynamic Programming (NDP) approach was proposed by Bertsekas and Tsitsiklis (1996). The NDP approach is to utilize all the data collected to generate an approximation of optimal cost-to-go function which was used to find the optimal input movement in real time control. The approximation could be any type of function such as polynomials, neural networks and etc. In this study, an algorithm using NDP approach was applied to a pH neutralization process to investigate the feasibility of the NDP algorithm and to deepen the understanding of the basic characteristics of this algorithm. As the global approximator, the neural network which requires training and k-nearest neighbor method which requires querying instead of training are investigated. The global approximator requires optimal control strategy. If the optimal control strategy is not available, suboptimal control strategy can be used even though the laborious Bellman iterations are necessary. For pH neutralization process it is rather easy to devise an optimal control strategy. Thus, we used an optimal control strategy and did not perform the Bellman iteration. Also, the effects of constraints on control moves are studied. From the simulations, the NDP method outperforms the conventional PID control.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.4
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• pp.403-410
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• 1999

In this study, a parallel algorithm has been developed that can quickly solve the optiaml control problem of large-scale dynamic systems. The algorithm adopts the sequential quadratic programming methods and achieves domain decomposition-type parallelism in computing sensitivities for search direction computation. A silicon wafer thermal process problem has been solved using the algorithm, and a parallel efficiency of 45% has been achieved with 16 processors. Practical methods have also been investigated in this study as a way to further speed up the computation time.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.6
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• pp.90-98
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• 1997

A time-optimal control law for quick, strongly nonlinear systems has been developed and demonstrated. This procedure involves the utilzation of neural networks as state feedback controllers that learn the time-optimal control actions by means of an iterative minimization of both the final time and the final state error for the systems with constrained inputs and/or states. A neural identifier or a genetic algorithm identifier could be utilized for modeling the partially known systems and the unknown systems. The nature of neural networks as a parallel processor would circumvent the problem of "curwe of dimensionality". The control law has been demonstrated for both a torque input motor and a velocity input motor identified by a genetic algorithm called GENOCOPed GENOCOP.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.904-913
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• 2005

This paper deals with an integrated problem of inventory control and dynamic pricing strategies for a commodity with price and sales-period dependent demand pattern, where a seller and customers have complete information of each other. The problem consists of two parts; one is each buyer's benefit problem which makes the best decision on price and time for buyer to purchase items, and the other one is a seller's profit problem which decides an optimal sales strategy concerned with inventory control and discount schedule. The seller's profit function consists of sales revenue and inventory holding cost functions. The two parts are closely related into each other with some related variables, so that any existing general solution methods can not be applied. Therefore, a simplified model with single seller and two customers in considered first, where demand for multiple units is allowed to each customer within a time limit. Therewith, the model is generalized for a n-customer-classes problem. To solve the proposed n-customer-set problem, a dynamic programming algorithm is derived. In the proposed dynamic programming algorithm, an intermediate profit function is used, which is computed in case of a fixed initial inventory level and then adjusted in searching for an optimal inventory level. This leads to an optimal sales strategy for a seller, which can derive an optimal decision on both an initial inventory level and a discount schedule, in $O(n^2)$ time. This result can be used for some extended problems with a small customer set and a short selling period, including sales strategy for department stores, Dutch auction for items with heavy holding cost, open tender of materials, quantity-limited sales, and cooperative buying in the on/off markets.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.272-275
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• 1997

When a manipulator makes contact with an object having position uncertainty, performance measures vary considerably with the control law. To achieve the optimal solution for this problem, an unique objective function that weights time and impact force is suggested and is solved with the help of variational calculus. The resulting optimal velocity profile is then modified to define a sliding mode for the impact and force control. The sliding mode control technique is used to achieve the desired performance. Sets of experiments are performed, which show superior performance compared to any existing controller.