• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.137-147
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• 2001

Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.10
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• pp.1000-1006
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• 2007

This paper presents an LMI-based method to design a saturated state-feedback $H_2$ controller for uncertain systems with actuator saturation. Specifically, the paper proposes a sufficient condition such that the system under norm-bounded uncertainties and actuator saturation is asymptotically stable and the $H_2$-norm of the system has an upper-bound. The resulting condition is further utilized to solve a convex optimization problem specified in the context of $H_2$-norm minimization, whose solution yields a saturated $H_2$ controller. A numerical example is presented to show the effectiveness of the proposed method.

• International Journal of Control, Automation, and Systems
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• v.4 no.4
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• pp.516-523
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• 2006

This paper is concerned with the $H_{\infty}$ control problem of 2-D discrete state delay systems described by the Roesser model. The condition for the system to have a specified $H_{\infty}$ performance is derived via the linear matrix inequality (LMI) approach. Furthermore, a design procedure for $H_{\infty}$ state feedback controllers is given by solving a certain LMI. The design problem of optimal $H_{\infty}$ controllers is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Simulation results are presented to illustrate the effectiveness of the proposed results.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.592-595
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• 1999

In this paper, we propose a unified method to solve the various robust filtering problem for a class of uncertain discrete time systems. Generally, to solve the robust filtering problem, we must convert the convex optimization problem with uncertainty blocks to the uncertainty free convex optimization problem. To do this, we derive the robust matrix inequality problem. This technique involves using constant scaling parameter which can be optimized by solving a linear matrix inequality problem. Therefore, the robust matrix inequality problem does not conservative. The robust filter can be designed by using this robust matrix inequality problem and by considering its solvability conditions.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.575-580
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• 1992

Mixed H$_{2}$/H$_{\infty}$ robust control synthesis is considered for finite dimensional linear time-invariant systems under the presence of diagonal structured uncertainties. Such uncertainties arise for instance when there is real perturbation in the nominal model of the state space system or when modeling multiple (unstructured) uncertainty at different locations in the feedback loop. This synthesis problem is reduced to convex optimization problem over a bounded subset of matrices as well as diagonal matrix having certain structure. For computational purpose, this convex optimization problem is further reduced into Generalized Eigenvalue Minimization Problem where a powerful algorithm based on interior point method has been recently developed..

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.129-132
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• 1999

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H$_2$and/or H$_{\infty}$ norms are used as criteria in an estimation error sense. In this paper, the mixed $H_2/H_{\infty}$ filtering Problem in lineal discrete-time systems is solved using the LMI approach, yielding a compromise between the H$_2$and H$_{\infty}$ filter designs. This filter design problems we formulated in a convex optimization framework using linear matrix inequalities. A numerical example is presented.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.2
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• pp.117-127
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• 2000

In this paper, we propose a new convex combination weight rule for the cross decomposition method which is known to be one of the most reliable and promising strategies for the large scale optimization problems. It is called generalized cross decomposition, a modification of linear mean value cross decomposition for specially structured linear programming problems. This scheme puts more weights on the recent subproblem solutions other than the average. With this strategy, we are having more room for selecting convex combination weights depending on the problem structure and the convergence behavior, and then, we may choose a rule for either faster convergence for getting quick bounds or more accurate solution. Also, we can improve the slow end-tail behavior by using some combined rules. Also, we provide some computational test results that show the superiority of this strategy to the mean value cross decomposition in computational time and the quality of bounds.

• Transactions of the Society of Information Storage Systems
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• v.3 no.2
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• pp.73-80
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• 2007

Atomic Force Microscopy (AFM)방식을 이용한 Scanning probe Data Storage (SDS) 시스템은 array cantilever 를 이용하여 나노 단위로 데이터 읽기, 쓰기를 하는 시스템이다. 따라서 미디어가 있는 stage 의 x 축과 y 축 및 두 축간 coupling 을 고려한 제어기 설계가 요구된다. 본 논문은 SDS 시스템의 축간 coupling 을 고려하지 않은 기존의 제안된 LQG 에 PI 를 추가한 제어기 구조를 사용한다. 두 축간 coupling 공진의 영향을 최소화 하기 위해 convex optimization 으로 설계된 최적의 position profile를 기준 입력신호로 사용한다. 제안된 제어기를 SDS 시스템에 적용하여 모의실험을 하고 그 결과 position profile 로 인해 각 축간 coupling 공진 영향이 감소하여 tracking performance 가 기존의 LQG 제어기 보다 향상된 것을 확인한다.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.750-753
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• 1998

This paper gives a simple parameterization of all stable unbiased filters to solve the suboptimal mixed $H_2/H_{\infty}$ filtering problem. Using the central filter, mixed $H_2/H_{\infty}$ filter is designed which minimizes the upper bound for the $H_2$ norm of the transfer matrix from a white noise to the estimation error subject to an $H_{\infty}$ norm constraint on the transfer matrix from an energy-bounded noise to the estimation error. The problem of finding suitable estimator gain can be converted into a convex optimization problem involving linear matrix inequalities.

• Transactions of the Society of Information Storage Systems
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• v.3 no.1
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• pp.28-33
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• 2007

최근 Hard Disk Drive(HDD)는 컴퓨터 산업의 발달과 함께 멀티미디어 어플리케이션의 요구에 따라 대용량화 추세에 있다. 이러한 대용량 HDD 는 고밀도, 고정밀의 track 정보가 필요하게 되고, 이는 HDD 생산에 고속, 고정밀의 Servo Track Writer(STW)를 필요로 하게 되었다. 그러나, 기존의 STW 는 PID 제어기에 공진 모드 제거를 위한 notch filter 를 사용하기 때문에 고속화에는 한계가 있어 track 정보를 기록하는 생산시간의 단축이 어렵다. 본 논문에서는 이를 위하여 기존의 STW 에 공진 모드의 여기를 최소화하기 위해 제어 입력의 profile 을 설계하는데 convex optimization 을 이용한 최적화 기법을 사용하였다. 이렇게 설계된 제어 입력은 플랜트의 공진 모드가 존재하는 주파수 대역에 에너지를 최소화시켜 공진 모드의 영향을 적게 받는다. 그 결과로 빠른 settling time 과 위치 정밀도가 향상된다. 그 효과는 모의 실험을 통해 검증하였다.