• East Asian mathematical journal
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• v.31 no.5
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• pp.737-742
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• 2015

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

• East Asian mathematical journal
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• v.31 no.3
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• pp.345-349
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• 2015

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

• East Asian mathematical journal
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• v.35 no.3
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• pp.289-296
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• 2019

We establish necessary and sufficient optimality conditions for a nonsmooth fractional robust optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• East Asian mathematical journal
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• v.32 no.5
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• pp.635-639
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• 2016

In this paper, we prove a sufficient optimality theorems for the problem(FP) under(V, ${\rho}$)-invexity assumption. And we give Mond-Weir type dual problem and proved weak and strong duality theorem under (V, ${\rho}$)-invexity

• ETRI Journal
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• v.36 no.3
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• pp.506-509
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• 2014

This paper studies the energy efficiency power allocation for cognitive radio networks based on uplink orthogonal frequency-division multiplexing. The power allocation problem is intended to minimize the maximum energy efficiency measured by "Joule per bit" metric, under total power constraint and robust aggregate mutual interference power constraint. However, the above problem is non-convex. To make it solvable, an equivalent convex optimization problem is derived that can be solved by general fractional programming. Then, a robust energy efficiency power allocation scheme is presented. Simulation results corroborate the effectiveness of the proposed methods.

• Journal of Power Electronics
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• v.19 no.4
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• pp.835-845
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• 2019

This paper presents a robust-optimal control strategy to improve the output-voltage error-tracking and control capability of a DC-DC boost converter. The proposed strategy employs an optimized Fractional-order Proportional-Integral (FoPI) controller that serves to eliminate oscillations, overshoots, undershoots and steady-state fluctuations. In order to significantly improve the error convergence-rate during a transient response, the FoPI controller is augmented with a pre-stage nonlinear error-modulator. The modulator combines the variations in the error and error-derivative via the signed-distance method. Then it feeds the aggregated-signal to a smooth sigmoidal control surface constituting an optimized hyperbolic secant function. The error-derivative is evaluated by measuring the output-capacitor current in order to compensate the hysteresis effect rendered by the parasitic impedances. The resulting modulated-signal is fed to the FoPI controller. The fixed controller parameters are meta-heuristically selected via a Particle-Swarm-Optimization (PSO) algorithm. The proposed control scheme exhibits rapid transits with improved damping in its response which aids in efficiently rejecting external disturbances such as load-transients and input-fluctuations. The superior robustness and time-optimality of the proposed control strategy is validated via experimental results.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.560-564
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• 1996

A mixed H$^{2}$/$H^{\infty}$ controller design method for linear systems with time delay in all variables and parameter uncertainties in all system matrices is proposed. Robust $H^{\infty}$ performance and H$^{2}$ performance condition that accounts for model-matching of closed loop system and disturbance rejection is also derived. With expressing uncertain system with linear fractional transformation form, we transform the robust stability and performance problem to the H$^{2}$/$H^{\infty}$ optimization problem and design a mixed H$^{2}$/$H^{\infty}$ controller. Using the proposed method, mixed H$^{2}$/$H^{\infty}$ controller for underwater vehicle with time delay and parameter variations are designed. Simulations of a design example with hydrodynamic parameter variations and disturbance are presented to demonstrate the achievement of good robust performance.t performance.ance.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1235-1242
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• 2006

Viscoelastic damping materials are widely used to reduce noise and vibration because of its low cost and easy implementation, for examples, on the body structure of passenger cars, air planes, electric appliances and ships. To design the damped structures, the material property such as elastic modulus and loss factor is essential information. The four-parameter fractional derivative model well describes the nonlinear dynamic characteristics of the viscoelastic damping materials with respect to both frequency and temperature with fewer parameters than conventional spring-dashpot models. However the identification procedure of the four-parameter is very time-consuming one. An efficient identification procedure of the four-parameters is proposed by using an FE model and a gradient-based numerical search algorithm. The identification procedure goes two sequential steps to make measured FRFs coincident with simulated FRFs: the first one is a peak alignment step and the second one is an amplitude adjustment. A numerical example shows that the proposed method is efficient and robust in identifying the viscoelastic material parameters of fractional derivative model.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.171-179
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• 2008

This paper addresses the synthesis of an iterative learning controller for a class of linear systems with norm-bounded parameter uncertainties. We take into account an iterative learning algorithm with current cycle feedback in order to achieve both robust convergence and robust stability. The synthesis problem of the developed iterative learning control (ILC) system is reformulated as the ${\gamma}$-suboptimal $H_{\infty}$ control problem via the linear fractional transformation (LFT). A sufficient convergence condition of the ILC system is presented in terms of linear matrix inequalities (LMIs). Furthermore, the ILC system with fast convergence rate is constructed using a convex optimization technique with LMI constraints. The simulation results demonstrate the effectiveness of the proposed method.

• Structural Engineering and Mechanics
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• v.67 no.1
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• pp.33-43
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• 2018

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.