• 대한전기학회논문지
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• 제31권7호
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• pp.18-24
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• 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.

• East Asian mathematical journal
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• 제27권1호
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• pp.91-100
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• 2011

It is important to find an optimal strategy which maximize the surplus of the insurance company at the maturity time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy, under the CEV model, which maximizes the expected exponential utility of the final value of the surplus at T. To do this optimization problem, the corresponding Hamilton-Jacobi-Bellman equation will be transformed a linear partial differential equation by applying a Legendre transform.

• 대한수학회지
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• 제59권2호
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• pp.311-335
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• 2022

This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.

• Structural Engineering and Mechanics
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• 제32권1호
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• pp.21-36
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• 2009

An importance sampling method is presented for computing the first passage probability of elasto-plastic structures under stochastic excitations. The importance sampling distribution corresponds to shifting the mean of the excitation to an 'adapted' stochastic process whose future is determined based on information only up to the present. A stochastic control approach is adopted for designing the adapted process. The optimal control law is determined by a control potential, which satisfies the Bellman's equation, a nonlinear partial differential equation on the response state-space. Numerical results for a single-degree-of freedom elasto-plastic structure shows that the proposed method leads to significant improvement in variance reduction over importance sampling using design points reported recently.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 추계학술대회 논문집 학회본부
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• pp.213-215
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• 1995

This paper is concerned with a coplanar pursuit-evasion game of one inertial evader and two identical noninertial pursuers. The terminal time is fired and the payoff is the distance between the evader and the nearest pursuer when tile game is terminated. The value functions and the strategies is constructed for all the game surface. To get a value function, we use the generalization of the Bellman-Isaacs fundamental equation.

• 대한수학회지
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• 제59권6호
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2023년도 춘계학술대회
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• pp.254-255
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• 2023

This paper discovers a robust managerial strategy for a stochastic inventory of perishable products, where the model experiences changing factors including inner parameters and an external disturbance with unknown form. An analytical solution for the optimization problem can be obtained by applying the Hamilton-Bellman-Jacobi equation, however the policy result cannot completely suppress the oscillation from the external disturbance. Therefore, an intelligent approach named Radial Basis Function Neural Networks is applied to estimate the unknown disturbance and provide a robust controller to manipulate the inventory level more effective. The final results show the outstanding performance of RBFNN controller, where both the estimation error and control error are guaranteed in the predefined limit.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.168-173
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• 2003

In this paper, we will present a deeper look on optimal design methods that are related to path-planning for a mobile robot. To control the motion of a mobile robot in a clustered environment, it's necessary to know a suitable trajectory assuming certain start and goal point. Up to now, there are many literatures that concern optimal path planning for an obstacle avoided mobile robot. Among those literatures, we have chosen 2 novel methods for our further analysis. The first approach [4] is based on HJB(Hamilton-Jacobi-Bellman) equation whose solution is the return-function that helps to generate a shortest path to the goal. The later [5] is called polynomial-path-planning approach, in this method, a shortest polynomial-shape path would become a solution if it was a collision-free path. The camera network plays the role as sensors to generate updated map which locates the static and dynamic objects in the space. Therefore, the exhibition of both path planning and dynamic obstacle avoidance by the updated map would be accomplished simultaneously. As we mentioned before, our research will include the motion control of a true mobile robot on those optimal planned paths which were generated by above algorithms. Base on the kinematic and dynamic simulation results, we can realize the affection of moving speed to the stable of motion on each generated path. Also, we can verify the time-optimal trajectory through velocity tuning. To simplify for our analysis, we assumed the obstacles are cylindrical circular objects with the same size.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.143-146
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• 1997

In this paper, we propose a fuzzy-supervised nonlinear H$_{\infty}$ controller which guarantees the robustness and has exact tracking performance for robot manipulator with system parameter uncertainty and exogenous disturbance, The proposed controller which is based on robotic H$_{\infty}$ controller has fuzzy supervisor which decides the optimal control input weighting value through fuzzy making-decision process. Owing to the fuzzy supervisor, The proposed controller can take the optimal control input. Then, we will apply the proposed controller to rigid robot manipulator to verify the performance of our controller.r.

• International Journal of Aeronautical and Space Sciences
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• 제7권1호
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• pp.65-72
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• 2006

A variable structure controller with an optimized sliding surface is proposed for slew maneuver of a rigid spacecraft. Rodrigues parameters are chosen to represent the spacecraft attitude. The quadratic type of performance index is used to design the sling surface. For optimization of the sliding surface, a Hamilton- Jacobi-Bellman equation is formulated and it is solved through the numerical algorithm using Galerkin approximation. The solution denotes a nonlinear sliding surface, on which the trajectory of the system satisfies the optimality condition approximately. Simulation result demonstrates that the proposed controller is effectively applied to the slew maneuver of a rigid spacecraft.