• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.321-341
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• 2013

In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k(k{\geq}0)$. Using mixed elliptic reconstruction method, a posterior $L^{\infty}(L^2)$-error estimates for both the state and the control approximation are derived. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

• International Journal of Control, Automation, and Systems
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• v.4 no.2
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• pp.146-154
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• 2006

In this paper, we propose direct and indirect adaptive fuzzy sliding mode control approaches for a class of nonaffine nonlinear systems. In the direct case, we use the implicit function theory to prove the existence of an ideal implicit feedback linearization controller, and hence approximate it to attain the desired performances. In the indirect case, we exploit the linear structure of a Takagi-Sugeno fuzzy system with constant conclusion to establish an affine-in-control model, and therefore design an indirect adaptive fuzzy controller. In both cases, the adaptation laws of the adjustable parameters are deduced from the stability analysis, in the sense of Lyapunov, to get a more accurate approximation level. In addition to their robustness, the design of the proposed approaches does not require the upper bounds of both external disturbances and approximation errors. To show the efficiency of the proposed controllers, a simulation example is presented.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.2
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• pp.59-65
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• 2000

In this paper the comparison of the first order approximation schemes such as SLP(sequential linear programming) CONLIN(convex linearization) MMA(method of moving asymptotes) and the second order approximation scheme SQP(sequential quadratic programming) was accomplished for optimization of nonlinear structures. It was found that MMA and SQP are the most efficient methods for optimization. But the number of function call of SQP is much more than that of MMA. Therefore when it is considered with the expense of computation MMA is more efficient than SQP. In order to examine the efficiency of MMA for complex optimization problem it was applied to the helicopter tail boom con-sidering column buckling and local wall buckling constraints. it is concluded that MMA can be a very efficient approxima-tion scheme from simple problems to complex problems.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1732-1733
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• 2011

This paper presents observer-based controller design for interval type-2 fuzzy system with staircase membership approximation. In type-2 fuzzy case, membership function is itself fuzzy set itself. Thus, type-2 fuzzy system can deal with parametric uncertainties of nonlinear system by capturing the uncertainties in membership function. Likewise, stabilization condition of type-2 fuzzy system is derived from quadratic Lyapunov function, and it goes to linear matrix inequality. Furthermore, in this paper, to relax the conservativeness of stabilization condition, staircase membership function approximating method is applied. Observer-based control method is adopted to control system which has some unmeasurable states. To prove suitability of our proposed method, numerical example is presented.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.6
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• pp.435-441
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• 2003

This paper addresses that an approximation and tracking control of realtime recurrent neural networks(RTRN) using two-dimensional iterative teaming algorithm for an electro-hydraulic servo system. Two dimensional learning rule is driven in the discrete system which consists of nonlinear output fuction and linear input. In order to control the trajectory of position, two RTRN with the same network architecture were used. Simulation results show that two RTRN using 2-D learning algorithm are able to approximate the plant output and desired trajectory to a very high degree of a accuracy respectively and the control algorithm using two identical RTRN was very effective to trajectory tracking of the electro-hydraulic servo system.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.632-634
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• 2000

The robust design of controllers to ensure gain and phase margin is can be use approximation of arctan function. In this paper, We proposed a tuning algorithm PID controllers based on specified gain and phase margin by a new approximation of arctan function. This method have linear interpolation equations of two arctan interval instead of one arctan interval of arctan(x). It is shown that the frequency response of this method was to ensure specified gain and phase margin.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.191-198
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• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.15-26
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• 2009

Bass diffusion model have played a central role in studying the diffusion of the new products since 1969, the year of publication of Bass model. Almost 750 publications based on the Bass diffusion model have explored extensions and applications. Extension models can be divided into two types. One is the model containing marketing-mix variables and the other is the model containing additional parameters. This paper presents another extension model of the latter type. Our model allows the time varying coefficients of innovation and imitation. Two pieces approximation of time varying coefficients is introduced and it's parameters are estimated based on NLS(Non-Linear Mean Square) method. Empirical studies are performed and the results show that our model is superior to the basic Bass model and the NUI(Non-Uniform Influence) model which is the well-known extension of the Bass model. The model developed in this paper is, also, transformed into the Bass model with the ready potential adopters in order to enhance the descriptive power.

• International Journal of Control, Automation, and Systems
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• v.1 no.2
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• pp.171-177
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• 2003

In this paper, we investigate a robust $H_{\infty}$ state feedback control technique for continuous time bilinear systems with an additive disturbance input. The nonlinear robust $H_{\infty}$control for bilinear systems requires a solution to the state dependent algebraic Riccati equation (SDARE). We present a new robust $H_{\infty}$control technique based on the successive approximation method for solving the SDARE by converting bilinear systems into time-varying linear systems. The proposed control method guarantees robust stability for closed loop bilinear systems. The proposed algorithm is verified by numerical examples.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.