• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1337-1358
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• 2018

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths $$-div\({\mid}{\nabla}u{\mid}^{p_1(x)-2}{\nabla}u\)-\sum\limits^n_{i=1}D_i\({\mid}u{\mid}^{p_0(x)-2}D_iu\)+c(x,u)=h(x),\;{\in}{\Omega}$$ in a bounded domain ${\Omega}{\subset}{\mathbb{R}}^n$. Here, one of the operators in the sum is monotone and the other is weakly compact. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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• pp.35-38
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• 1998

Abstracts In this paper, we propose a robust adaptive fuzzy control scheme using a sliding control input for tracking of a class of MISO nonlinear systems with unknown bounded external disturbances. In the proposed scheme, the nonlinearity is estimated adaptively via a fuzzy inference based on a fuzzy model. A sliding control input is introduced such that boundedness of all signals in the system is guaranteed even though the existence of a fuzzy approximation error and external disturbances. The controller parameters are updated by using a proposed adaptation law, which is similar 1-modification method. Computer simulation shows the effectiveness of the proposed control scheme.

• Proceedings of the KIPE Conference
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• 2005.07a
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• pp.697-700
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• 2005

An adaptive fuzzy sliding-mode controller (SMC) for uncertain or ill-defined single-input single-output (SISO) nonaffine nonlinear systems is proposed. By using the universal approximation property of the fuzzy logic system (FLS), it is tuned on-line to cancel the unknown system nonlinearity. We adopt a self-structuring FLS to guarantee global stability of the closed-loop system rather than semi=global boundedness. The control and adaptive laws are derived so that the estimated fuzzy parameters are bounded and the sliding condition is satisfied.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.5
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• pp.315-322
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• 2004

A direct adaptive state-feedback controller for highly nonlinear systems is proposed. This paper considers uncertain or ill-defined nonaffine nonlinear systems and employs a static fuzzy logic system (FLS). The employed FLS estimates. and adaptively cancels an unknown plant nonlinearity using its proved universal approximation property. A control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed-loop system is stable in the sense of Lyapunov. The tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term. No a priori knowledge of an upper bound on an lumped uncertainty is required.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.137-151
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• 2023

In this paper we prove the existence of nontrivial weak solutions to the boundary value problem -G₁u = u³ + f(x, y, u) in Ω, u ≥ 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain with smooth boundary in ℝ³, G₁ is a Grushin type operator, and f(x, y, u) is a lower order perturbation of u³ with f(x, y, 0) = 0. The nonlinearity involved is of critical exponent, which differs from the existing results in [11, 12].

• Journal of Astronomy and Space Sciences
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• v.22 no.1
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• pp.21-34
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• 2005

The initial conditions that generate bounded motion in eccentric reference orbit are determined for satellite formation flying. Because Hill's equations cannot describe the relative motion between two satellites in eccentric orbit, a new relative dynamics utilizing the nonlinearity and eccentricity correction for Hill's initial conditions is implemented. The constraint that matches angular rates of chief and deputy satellites is used to obtain the bounded motion between them. The constraint can be applied to satellite formation motions in eccentric orbit, since it implicates J2 perturbation due to the central body's aspherical gravitational forces. The periodic bounded motions are analyzed for the orbit with the eccentricity of less than 0.05 and about 0.5 km relative distance between chief and deputy satellites. It is mainly illustrated that the satellite formations in small eccentric orbits can have hounded motions; consequently, the formation can be kept by matching angular rates of the satellites. These results demonstrate an useful method that reduces the cost for operating satellites by providing effective initial conditions for satellite formation flying in eccentric orbit.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.375-382
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• 2004

This paper presents control designs using neural networks (NN) for a XY positioning table. The proposed neuro-controller is composed of an outer PD tracking loop for stabilization of the fast flexible-mode dynamics and an NN inner loop used to compensate for the system nonlinearities. A tuning algorithm is given for the NN weights, so that the NN compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded weight estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The proposed neuro-controller is implemented and tested on an IBM PC-based XY positioning table, and is applicable to many precision XY tables. The algorithm, simulation, and experimental results are described. The experimental results are shown to be superior to those of conventional control.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.527-532
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• 2005

In this paper, we proposed an adaptive fuzzy sliding control for unknown nonlinear systems using estimation of bounds for approximation errors. Unknown nonlinearity of a system is approximated by the fuzzy logic system with a set of IF-THEN rules whose consequence parameters are adjusted on-line according to adaptive algorithms for the purpose of controlling the output of the nonlinear system to track a desired output. Also, using assumption that the approximation errors satisfy certain bounding conditions, we proposed the estimation algorithms of approximation errors by Lyapunov synthesis methods. The overall control system guarantees that the tracking error asymptotically converges to zero and that all signals involved in controller are uniformly bounded. The good performance of the proposed adaptive fuzzy sliding mode controller is verified through computer simulations on an inverted pendulum system.

• International Journal of Computer Science & Network Security
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• v.22 no.4
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• pp.1-12
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• 2022

In order to overcome the power fluctuation issues in photovoltaic (PV) smart grid-connected systems and the inverter nonlinearity model problem, an adaptive backstepping command-filter and a double second order generalized Integrators (DSOGI) controller are designed in order to tune the AC current and the DC-link voltage from the DC side. Firstly, we propose to present the filter mathematical model throughout the PV system, at that juncture the backstepping control law is applied in order to control it, Moreover the command filter is bounded to the controller aiming to exclude the backstepping controller differential increase. Additionally, The adaptive law uses Lyapunov stability criterion. Its task is to estimate the uncertain parameters in the smart grid-connected inverter. A DSOGI is added to stabilize the grid currents and eliminate undesirable harmonics meanwhile feeding maximum power generated from PV to the point of common coupling (PCC). Then, guaranteeing a dynamic effective response even under very unbalanced loads and/or intermittent climate changes. Finally, the simulation results will be established using MATLAB/SIMULINK proving that the presented approach can control surely the smart grid-connected system.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.4
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• pp.93-102
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• 1989

A runoff model is estabilished for the direct runoff hydrograph at the watershed outlet. The watershed is divided into subareas bounded by watershed lines of stream segment. Different storage elements are used to represent the subareas which simply translate rain-fall excess to runoff and transmit flow from an upstream areas. For transmit, the relationship between flowsection and runoff is expressed by the exponential function to represent the nonlinearity of lag time, and the relationship between flowsection and stream length is expressed by the 1st order equation to represent the effect of the travel length. The parameters of lag time can be obtained by stream magnitude and the effective rain fall is routed through the main stream. Application of the model to the Bochung river basin gives accurate results, especially for the peak runoff and peak time, and is approved to be used for the prediction by stream magnitude of small watershed having no runoff records.