• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.170-177
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• 1998

In this paper, a unified solution of Hankel norm approximation problem is proposed by $\delta$-operator. To derive the main result, all-pass property is derived from the inner and co-inner property in the $\delta$-domain. The solution of all-pass becomes an optimal Hankel norm approximation problem in .delta.-domain through LLFT(Low Linear Fractional Transformation) inserting feedback term $\phi(\gamma)$, which is a free design parameter, to hold the error bound desired against the variance between the original model and the solution of Hankel norm approximation problem. The proposed solution does not only cover continuous and discrete ones depending on sampling interval but also plays a key role in robust control and model reduction problem. The verification of the proposed solution is exemplified via simulation for the zero-order Hankel norm approximation problem and the model reduction problem applied to a 16th order MIMO system.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.3
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• pp.256-263
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• 2013

The saturation of the actuator impairs the response performance of the near space interceptor control system. A control system based on the properties of linear tracking system is designed for this problem. The properties are that the maximum value of the pseudo-Lyapunov function of the linear tracking control system do not present at the initial state but at the steady state, based on which the bounded stability problem is converted into linear tracking problem. The pseudo-Lyapunov function of the linear tracking system contain the input variables; the amplitude and frequency of the input variables affect the stability of the nonlinear control system. Designate expected closed-loop poles area for different input commands and obtain a controller which is function of input variables. The coupling between variables and linear matrices make the control system design problem non-convex. The non-convex problem is converted into a convex LMI according to the Shur complement lemma and iterative algorithm. Finally the simulation shows that the designed optimal control system is quick and accurate; the rationality of the presented design techniques is validated.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.772-776
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• 1988

In quantized control systems, the control values can take only given discrete (e.g. integer) values. In case of dealing with the control problem on the discrete-time, final-stage fixed, quantized control systems with multidimensional performance functions, the first thing, new definition on noninferior solutions in these systems is necessary because of their discreteness in state variables, and the efficient search for those solutions at final-stage is unavoidable for seeking their discrete-time optimal controls to these systems. In this paper, to the quantized control problem given by the formulation of Halkin-typed linear control systems with two performance functions, a new definition on noninferior solutions of this system control problem and a heuristic effective search on these noninferior solutions are stated. By use of these concepts, two definitions on noninferior solutions and the algorithm consisted of 8 steps and attained by geometric approaches are given. And a numerical example using the present algorithm is shown.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.5
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• pp.57-68
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• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• Journal of the Korea institute for structural maintenance and inspection
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• v.12 no.5
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• pp.179-189
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• 2008

The object of this study is to develope a program with proposed numerical techniques for an optimal seismic control of structures using active tendon systems. Ricatti closed-loop algorithm has been applied to control the active tendon systems with time-delay problem. The optimal control is formulated as an optimization problem which is finding optimal weighting matrices by minimizing the quadratic performance index by SUMT. In order to find the optimal location of active tendons in structures, controllability index has been introduced. From numerical examples, the current optimal control technique with optimal location of tendons was suitable to control the seismic response of structures.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.327-337
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• 2015

This paper is concerned with the optimality conditions for optimal control problem of Belousov-Zhabotinskii reaction model. That is, we obtain the optimality conditions by showing the differentiability of the solution with respect to the control. We also show the uniqueness of the optimal control.

• 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.

• IE interfaces
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• v.24 no.4
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• pp.396-407
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• 2011

We develop a cash management model in which firms face randomly occurred investment projects and retrieve investments upon the maturity of these projects. Using the Markov Decision Problem approach, we examine a control policy which dynamically adjusts the cash balance under the discounted cost criterion. The existence of an optimal policy is shown under some conditions. The optimal solution procedure is developed to find the optimal points and the optimal sizes for adjusting the cash balance. In numerical experiment, we investigate important structural properties of the optimal cash management policy.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.2
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• pp.153-159
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• 2004

A control-structure combined optimal design problem is discussed taking a 3-D truss structure as a design object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. We consider not only minimum weight design problem for structure system, but also suppression problem of the effect of disturbances for control system as the purpose of the design. By minimizing the linear sum of the normalized structural objective function and control objective function, it is possible to make optimal design by which the balance of the structural weight and the control performance is taken.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.156.2-156
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• 2001

Hypersonic civil airplanes are recently heated up again in USA and Japan, but there are several difficulties when we obtain its optimal trajectories. In this paper, we formulated the trajectory optimization problem as an optimal control problem and solved it by the direct shooting method with the Genetic Algorithm, GA. The result shows it is effective to use this method for the trajectory optimization of the hypersonic flight.