• East Asian mathematical journal
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• v.17 no.2
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.539-544
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• 1992

An iterative lear-rung control scheme is newly designed in tile frequency domain. Purposing for batch process control, a generic form of feedback-assisted first-order learning is considered first, and the inverse model-based learning algorithm is derived through convergence analysis in the frequency domain. To enhance the robustness of the proposed scheme, a filtered version is also presented. Performance of the proposed scheme is evaluated through numerical simulations.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.731-742
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• 2022

In this paper, we present a new mixed type iterative process for approximating the common fixed points of single-valued nonexpansive mapping and multi-valued nonexpansive mapping in a CAT(0) space. We demonstrate strong and weak convergence theorems for the new iterative process in CAT(0) spaces, as well as numerical results to support our theorem.

• The Mathematical Education
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• v.30 no.1
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• pp.35-42
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• 1991

Multiobjective Optimisation problem involving set functions is introduced. Then an iterative algorithm for these kinds of problems is suggested and its optimal process will be proved.

• Current Optics and Photonics
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• v.5 no.3
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• pp.322-328
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• 2021

In this paper, a pretreatment method for a matrix in convex optimization is proposed to optimize the spectral reconstruction process of a disordered dispersion spectrometer. Unlike the reconstruction process of traditional spectrometers using Fourier transforms, the reconstruction process of disordered dispersion spectrometers involves solving a large-scale matrix equation. However, since the matrices in the matrix equation are obtained through measurement, they contain uncertainties due to out of band signals, background noise, rounding errors, temperature variations and so on. It is difficult to solve such a matrix equation by using ordinary nonstationary iterative methods, owing to instability problems. Although the smoothing Tikhonov regularization approach has the ability to approximatively solve the matrix equation and reconstruct most simple spectral shapes, it still suffers the limitations of reconstructing complex and irregular spectral shapes that are commonly used to distinguish different elements of detected targets with mixed substances by characteristic spectral peaks. Therefore, we propose a special pretreatment method for a matrix in convex optimization, which has been proved to be useful for reducing the condition number of matrices in the equation. In comparison with the reconstructed spectra gotten by the previous ordinary iterative method, the spectra obtained by the pretreatment method show obvious accuracy.

• Journal of Korean Society for Quality Management
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• v.40 no.4
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• pp.481-496
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• 2012

Purpose: This paper aims at improving inefficiency of an existing posterior preference articulation method proposed for dual response surface optimization. The method generates a set of non-dominated solutions and then allows a decision maker (DM) to select the best solution among them through an interval selection strategy. Methods: This paper proposes an iterative posterior preference articulation method, which repeatedly generates the predetermined number of non-dominated solutions in an interval which becomes gradually narrower over rounds. Results: The existing method generates a good number of non-dominated solutions not used in the DM's selection process, while the proposed method generates the minimal number of non-dominated solutions necessitated in the selection process. Conclusion: The proposed method enables a satisfactory compromise solution to be achieved with minimal cognitive burden of the DM as well as with light computation load in generating non-dominated solutions.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.299-302
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• 1996

A control algorithm is proposed for nonlinear multi-input multi-output(MIMO) batch processes by combining quadratic iterative learning control(Q-ILC) with model predictive control(MPC). Both controls are designed based on output feedback and Kalman filter is incorporated for state estimation. Novelty of the proposed algorithm lies in the facts that, unlike feedback-only control, unknown sustained disturbances which are repeated over batches can be completely rejected and asymptotically perfect tracking is possible for zero random disturbance case even with uncertain process model.

• Macromolecular Research
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• v.14 no.3
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• pp.287-299
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• 2006

To successively synthesize star-branched polymers, we developed a new iterative methodology which involves only two sets of the reactions in each iterative process: (a) an addition reaction of DPE or DPE-functionalized polymer to a living anionic polymer, and (b) an in-situ reaction of 1-(4-(4-bromobutyl)phenyl)-1-phenylethylene with the generated 1,1-diphenylalkyl anion to introduce one DPE functionality. With this methodology, 3-, 4-, and 5-arm, regular star-branched polystyrenes, as well as 3-arm ABC, 4-arm ABCD, and a new 5-arm ABCDE, asymmetric star-branched polymers, were successively synthesized. The A, B, C, D, and E arm segments were poly(4-trimethylsilylstyrene), poly(4-methoxystyrene), poly(4-methylstyrene), polystyrene, and poly(4-tert-butyldimethylsilyloxystyrene), respectively. All of the resulting star-branched polymers were well-defined in architecture and precisely controlled in chain length, as confirmed by SEC, $^1H$ NMR, VPO, and SLS analyses. Furthermore, we extended the iterative methodology by the use of a new functionalized DPE derivative, 1-(3-chloromethylphenyl)-1-((3-(1-phonyletheny1)phenyl) ethylene, capable of introducing two DPE functionalities via one DPE anion reaction site in the reaction (b). The number of arm segments of the star-branched polymer synthesized by the methodology could be dramatically increased to 2, 6, and up to 14 by repeating the iterative process.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.59 no.1
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• pp.29-34
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• 2010

This paper presents an intelligent learning controller for repetitive walking motion of biped walking robot. The proposed learning controller consists of an iterative learning controller and a direct learning controller. In the iterative learning controller, the PID feedback controller takes part in stabilizing the learning control system while the feedforward learning controller plays a role in compensating for the nonlinearity of uncertain biped walking robot. In the direct learning controller, the desired learning input for new joint trajectories with different time scales from the learned ones is generated directly based on the previous learned input profiles obtained from the iterative learning process. The effectiveness and tracking performance of the proposed learning controller to biped robotic motion is shown by mathematical analysis and computer simulation with 12 DOF biped walking robot.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.499-502
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• 1996

In this paper, we propose a fuzzy iterative learning controller(FILC). It can control fully unknown dynamic plants through iterative learning. To design learning controllers based on the steepest descent method, it is one of the difficult problems to identify the change of plant output with respect to the change of control input(.part.e/.part.u). To solve this problem, we propose a method as follows: first, calculate .part.e/.part.u using a similarity measure and information in consecutive time steps, then adjust the fuzzy logic controller(FLC) using the sign of .part.e/.part..u. As learning process is iterated, the value of .part.e/.part.u is reinforced. Proposed FILC has the simple architecture compared with previous other controllers. Computer simulations for an inverted pendulum system were conducted to verify the performance of the proposed FILC.