• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.99-107
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• 2007

We consider (worst-case) robust optimization versions of the Economic Order Quantity (EOQ) model with decreasing cost functions. Two variants of the EOQ model are discussed, in which the purchasing costs are decreasing power functions in either the order quantity or demand rate. We develop the corresponding worst-case robust optimization models of the two variants, where the parameters in the purchasing cost function of each model are uncertain but known to lie in an ellipsoid. For the robust EOQ model with the purchasing cost being a decreasing function of the demand rate, we derive the analytical optimal solution. For the robust EOQ model with the purchasing cost being a decreasing function of the order quantity, we prove that it is a convex optimization problem, and thus lends itself to efficient numerical algorithms.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.1
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• pp.31-35
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• 1999

In this paper, we consider the robust pole assignment and the upper bound of quadratic cost function for the linear systems with time-varying uncertainy. The considered uncertainties are both the norm bounded unstructured case and the structured case that has the matrix polytope type uncertain structure. We derve conditions that guarantee the robust pole assignment inside a disk in the L.H.P. and the robust stability. Also, we derive the upper bound of quadratic cost for thil pole assigned systems. Finally, we show the usefulness of our results by an example.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.589-592
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• 1996

It is well known that robust compensators designed by the block-diagonal Lyapunov function approaches are conservative while they are popular in practice because of their computational easiness. In this note, we develop a systematized version of conventional block-diagonal Lyapunov function approaches by deriving two separated optimizations based on the guaranteed cost control method. The proposed method generates reasonable robust compensators in practice.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.203-207
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• 1992

In this paper, a new GPC(Generalized Predictive Control) algorithm which is robust to disturbances isproposed. This controller minimizes the LQ cost function when the disturbance maximizes this cost function. The solution is obtained from the min-max problem which can be solved by differential game theory and has the non-recursive form which does not use the Riccati equation. Its another solution for state space models is investigated.

• Management Science and Financial Engineering
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• v.18 no.2
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• pp.23-27
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• 2012

The problem of jointly determining a robust optimal bundle of price and order quantity for a retailer in a single-retailer, single supplier, single-product supply chain is considered. Demand is modeled as a decreasing power function of product price, and unit purchasing cost is modeled as a decreasing power function of order quantity and demand. Parameters defining the two power functions are uncertain but their possible values are characterized by ellipsoids. We extend a previous study in two ways; the purchasing cost function is generalized to take into account the economies of scale realized by higher product demand in addition to larger order quantity, and an exact transformation into an equivalent convex optimization program is developed instead of a geometric programming approximation scheme proposed in the previous study.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.936-938
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• 1996

The $H_{\infty}$ robust controller is designed for on-line adaptive control application by using polynomial approach. The $H_{\infty}$ robust controllers for adaptive system were designed first by Grimble. But they have a problem that two minimum costs can exist and did not minimize the conventional $H_{\infty}$ cost function which is the $H_{\infty}$ sum of weighted sensitivity and complementary sensitivity terms. In this paper, the two minimum costs problem can be avoided and the conventional $H_{\infty}$ cost function is minimized by employing the Youla parameterization and polynomial approach at the same time. In addition pole placement is possible without any relation with weighting function.

• Journal of Communications and Networks
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• v.14 no.3
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• pp.237-242
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• 2012

One of the major problems for accurate channel estimation in power line communication systems is impulsive noise. Traditional channel estimation algorithms are based on the assumption of Gaussian noise, or the need to locate the positions of impulsive noise. The algorithms may lose optimality when impulsive noise exists in the channel, or if the location estimation of impulsive noise is inaccurate. In the present paper, an effective channel estimation algorithm based on a robust cost function is proposed to mitigate impulsive noise. The proposed method can provide a closed-form solution, and the application of robust estimation theory enables the proposed method to be free from localization of impulsive noise and thus can guarantee that the proposed method has better performance. Simulations verified the proposed algorithm.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.5
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• pp.535-543
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• 2014

In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.6 s.99
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• pp.680-686
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• 2005

This paper introduces the robust design of an intake system using transmission loss and the frequency weighting function. First, transmission loss is measured to evaluate the performance of the noise reduction for the intake system. The robust design parameters of the intake system are extracted by adapting a cost function with the Taguchi method. Subsequently, the frequency weighting function is developed by the subjective evaluation in which 6 special engineers were participated. Finally, the comparison between the proposed frequency weighted optimal design and unweighted optimal design for the transmission loss as the part is performed. Here, the overall levels of the transmission loss according to the methods are presented to validate the effectiveness of the proposed methodology.

• Journal of Power Electronics
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• v.19 no.2
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• pp.497-508
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• 2019

The predictive speed control (PSC) strategy can realize the simultaneous control of speed and current by using one cost function. As a model-based control method, the performance of the PSC is vulnerable to model mismatches such as load torque disturbances and parameter uncertainties. To solve this problem, this paper presents a robust predictive speed control (RPSC) strategy for surface-mounted permanent magnet synchronous motor (SPMSM) drives. The proposed RPSC uses extended state observers (ESOs) to estimate the lumped disturbances caused by load torque changes and parameter mismatches. The observer-based prediction model is then compensated by using the estimated disturbances. The introduction of ESOs can achieve robustness against predictive model uncertainties. In addition, a modified cost function is designed to further suppress load torque disturbances. The performance of the proposed RPSC scheme has been corroborated by experimental results under the condition of load torque changes and parameter mismatches.