• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.195-198
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• 1995

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is the most well-known and provides precise and rigorous theoretical backgrounds. However, tile conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, it is required to consider the damping effects. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. This method tan be utilized as a powerful tool to determine the region of attraction.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.597-610
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• 2010

For a class of nonlinear bilevel programming problems in which the follower's problem is linear, the paper develops a genetic algorithm based on the optimality conditions of linear programming. At first, we denote an individual by selecting a base of the follower's linear programming, and use the optimality conditions given in the simplex method to denote the follower's solution functions. Then, the follower's problem and variables are replaced by these optimality conditions and the solution functions, which makes the original bilevel programming become a single-level one only including the leader's variables. At last, the single-level problem is solved by using some classical optimization techniques, and its objective value is regarded as the fitness of the individual. The numerical results illustrate that the proposed algorithm is efficient and stable.

• Computers and Concrete
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• v.2 no.1
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• pp.55-77
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• 2005

The closed form solution of the equilibrium equations in the ultimate design of reinforced concrete sections under biaxial bending is presented. The stresses in the materials are described by the Model Code 1990 equations. Computation of the integral equations is performed generally in terms of all variables. The deformed shape of the section in the ultimate conditions is defined by Heaviside functions. The procedure is convenient for the use of mathematical manipulation programs and the results are easily included into nonlinear analysis codes. The equations developed for rectangular sections can be applied for other sections, such as T, L, I for instance, by decomposition into rectangles. Numerical examples of the developed model for rectangular sections and composed sections are included.

• East Asian mathematical journal
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• v.27 no.3
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• pp.319-337
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• 2011

We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.219-229
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• 2006

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term $$a(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)^{\prime}+p(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)+q(t)f(x(t))=0,\;{\sigma}>1$$, where the functions $a,\;p$ and $q$ are real-valued continuous functions defined on $[t_o,{\infty})$ with $a(t)>0,\;f(x){\in}C^1(\mathbb{R})$ and $\frac{f^{\prime}(u)}{|f^{({\sigma}-1)/{\sigma}}(u)|}{\geq}k>0$ for $u{\neq}0$.

• Bulletin of the Korean Chemical Society
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• v.9 no.1
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• pp.36-40
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• 1988

The time correlation functions of concentration fluctuations due to the random forces near the steady state are evaluated for a general two-component nonlinear chemical system by solving the corresponding two dimensional Fokker-Planck equation. The approximate method of solving the Fokker-Planck equation is based on the eigenfunction expansion and the corresponding eigenvalues for both the linear and nonlinear Fokker-Planck operators are obtained near the steady state. The general results are applied to the Lotka model near the oscillatory marginal steady state and the comparison is made between linear and nonlinear cases.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.9
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• pp.719-727
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• 2002

We proposed a decoupled adaptive fuzzy sliding-mode control scheme for a class of fourth-order nonlinear systems. The system is decoupled into two second-order systems such that each subsystem has a separate control target expressed in terms of sliding surface. For these sliding surfaces, we define main and sub target conditions. and, we made intermediate variables which are interconnected both surface conditions from the sub target sliding surface. Then, Two sets of fuzzy rule bases are utilized to represent the equivalent control input with unknown system functions of the main target sliding surface including intermediate variables. The membership functions of the THEN-part, which is used to construct a suitable equivalent control of sliding-mode control, are changed according to the adaptive law. With such a design scheme, we not only maintain the distribution of membership functions over state space but also reduce the computing time considerably. We apply the decoupled adaptive sliding-mode control to a nonlinear Cart-Pole system and confirms the validity of the proposed approach.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.689-693
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• 2000

In this paper, we proposed a decoupled adaptive fuzzy sliding-mode control scheme in designing the SMC of a class of fourth-order nonlinear systems. These systems are decoupled the whole system into two second-order systems such that each subsystem has a separate control target expressed in terms of a sliding surface. Then, information from the secondary target conditions the main target, which, in turn, generates a control action to make both subsystem move toward their sliding surface. respectively, and Two sets of fuzzy rule bases are utilized to represent the equivalent control input with unknown system functions of the main target, The membership functions of the THEN-part. which is used to construct a suitable equivalent control of SMC. are changed according to adaptive law, Under this design scheme, we not only maintain the distribution of membership functions over state space but also reduce considerably computing time, we apply the decoupled adaptive sliding-mode control to control a nonlinear inverted pendulum system and confirms the validity of the proposed approach.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1593-1600
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• 2000

A method based on frequency domain approaches is presented for the nonlinear parameters identification of structure having nonlinear joints. The finite element model of linear substructure is us ed to calculating its frequency response functions needed in parameter identification process. This method is easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of finite element model. Since this method is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude but also selecting excitation frequencies. The validity of this method is tested numerically and experimentally with a cantilever beam having the nonlinear element. It was verified through examples that the method is useful to identify the nonlinear parameters of a structure having arbitary nonlinear boundaries.

• The KSFM Journal of Fluid Machinery
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• v.14 no.2
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• pp.29-34
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• 2011

Aerodynamic torque of wind turbine is highly nonlinear due to the nonlinear interactions between wind and blade. The aerodynamic nonlinearity is represented by nonlinear power and torque coefficients which are functions of wind speed, rotational speed of rotor, and pitch angle of blade. It is essential from the viewpoint of understanding and analysis of dynamic characteristics for wind turbine to linearize the aerodynamic torque and define aerodynamic nonlinear parameters as derivatives of aerodynamic torque with respect to the three parameters. In this paper, a linearization method of the aerodynamic torque from power coefficient is presented through differentiating it by the three parameters. And steady-state values of three aerodynamic nonlinear parameters according to wind speed are obtained and their nonlinear characteristics are investigated.