• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.235-252
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• 2015

Optimal impact angle control guidance law and its variants for intercepting a maneuvering target are introduced in this paper. The linear quadratic(LQ) optimal control theory is reviewed first to setup framework of guidance law derivation, called the sweep method. As an example, the inversely weighted time-to-go energy optimal control problem to obtain the optimal impact angle control guidance law for a fixed target is solved via the sweep method. Since this optimal guidance law is not applicable for a moving target due to the angle mismatch at the impact instant, the law is modified to three different biased proportional navigation(PN) laws: the flight path angle control law, the line-of-sight(LOS) angle control law, and the relative flight path angle control law. Effectiveness of the guidance laws are verified via numerical simulations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.3
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• pp.451-458
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• 2012

This paper addresses the problem that policy iteration (PI) for continuous-time (CT) systems requires explorations of the state space which is known as persistency of excitation in adaptive control community, and as a result, proposes a PI scheme explorized by an additional probing signal to solve the addressed problem. The proposed PI method efficiently finds in online fashion the related CT linear quadratic (LQ) optimal control without knowing the system matrix A, and guarantees the stability and convergence to the LQ optimal control, which is proven in this paper in the presence of the probing signal. A design method for the probing signal is also presented to balance the exploration of the state space and the control performance. Finally, several simulation results are provided to verify the effectiveness of the proposed explorized PI method.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.293-312
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• 2015

We deal with a boundary control problem for the vorticity minimization, in which the ow is governed by the time-dependent two dimensional incompressible Navier-Stokes equations. We derive a mathematical formulation and a process for an appropriate control along the portion of the boundary to minimize the vorticity motion due to the ow in the fluid domain. After showing the existence of an optimal solution, we derive the optimality system for which optimal solutions may be determined. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solutions.

• Aerospace Engineering and Technology
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• v.7 no.1
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• pp.61-67
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• 2008

To design flight control law of an unmanned aerial vehicle, automated control gain determination program was developed. The procedure for determination of control gain was formulated as the control gains were designed from the optimal solutions of the optimization problem. PSO algorithm, which is one of the evolutionary computation method, and SQP algorithm, which is one of the nonlinear programming method, are used as optimization problem solver. Thru this technique, computation time required for finding the optimal solution is decreased to 1/5 of that of PSO algorithm and more accurate optimal solution is obtained.

• 전기의세계
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• v.28 no.2
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• pp.55-60
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• 1979

In this paper, a new method of the optimal control of the regulator and tracking control problem concerning the dimension of the velocity is derived and applied for the second order plant. The output position, output velocity and the control effort are plottcd with time applying analog computer simulation. And it is compared with the output of the ordinary optimal control law in case the reference input is given by velocity function, and studied about the gain of this method.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.11
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• pp.1065-1070
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• 2004

Optimal collision avoidance algorithm for unmanned aerial vehicles based on proportional navigation guidance law is investigated this paper. Although proportional navigation guidance law is widely used in missile guidance problems, it can be used in collision avoidance problem by guiding the relative velocity vector to collision avoidance vector. The optimal navigation coefficient can be obtained if an obstacle if an obstacle moves at constant velocity vector. The stability of the proposed algorithm is also investigated. The stability can be obtained by choosing a proper navigation coefficient.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• International Journal of Automotive Technology
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• v.6 no.1
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• pp.71-77
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• 2005

This paper presents a systematic approach which determines the optimal period to minimize performance measure subject to the schedulability constraints of a real-time control system by formulating the scheduling problem as an optimal problem. The performance measure is derived from the summation of end-to-end response times of processed I/Os scheduled by the static cyclic method. The schedulability constraint is specified in terms of allowable resource utilization. At first, a uniprocessor case is considered and then it is extended to a distributed system connected through a communication link, local-inter network, UN. This approach is applied to the design of an automotive body control system in order to validate the feasibility through a real example. By using the approach, a set of optimal periods can easily be obtained without complex and advanced methods such as branch and bound (B&B) or simulated annealing.

• Journal of Astronomy and Space Sciences
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• v.25 no.3
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.