• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2006.11a
• /
• pp.716-720
• /
• 2006

In order to examine the effect of constant excitation on nonlinear interactions in vibrating modes of circular plates, we added a constant term to a harmonic excitation. A two-degree-of freedom system is derived by using the Galerkin's procedure. The system is shown to have quadratic and cubic nonlinearities subjected to a harmonic excitation.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.3
• /
• pp.459-465
• /
• 2012

In this paper, we present a non-fragile guaranteed cost control design method for uncertain nonlinear systems with time varying delays in state and control input, even though the controller gain is perturbed. The uncertain nonlinear term in the systems is norm bounded and the linear matrix inequality(LMI) optimization method is employed as a stability analysis of the systems. We design a robust controller and show the asymptotical stability of uncertain time-varying systems based on Lyapunov method. Also, we guarantee a specific level of performance of the systems. The simulations are carried out to demonstrate the effectiveness of the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.4
• /
• pp.283-300
• /
• 2019

In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.

• Proceedings of the KIEE Conference
• /
• 1998.11b
• /
• pp.407-409
• /
• 1998

This paper deals with temporal-difference learning that is a method for approximating long-term future cost as a function of current state in knowlege-poor environment, a function approximator is used to approximate the mapping from state to future cost, a linear function approximator is limited because mapping from state to future cost has a nonlinear characteristic, so a nonlinear function approximator is used to approximate the mapping from state to future cost in this paper, and that TD learning using a nonlinear function approximator is stable is proved.

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

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.45 no.4
• /
• pp.582-589
• /
• 1996

In this paper, an adaptive control problem of a hydraulic actuator for vehicle active suspension controller is divided into two parts: the inner loop controller and the outer loop controller. Inner loop controller, which is a nonlinear adaptive controller, is designed to control the force generated by the nonlinear hydraulic actuator acting under the effects of Coulomb friction. For simplicity of designing a nonlinear controller, the spool valve dynamics of a hydraulic actuator is reduced using a singular perturbation technique. The estimation error signal used to an indirect parameter adaptation is calculated without a regressor filtering. The absolute velocity of a sprung mass will be damped down by its negatively proportional term(sky-hook damper) adopted as an outer loop controller. Simulation results are presented to show the importance of controlling the actuator force and the validity of the proposed adaptive controller. (author). refs., figs. tab.

• Communications of the Korean Mathematical Society
• /
• v.26 no.4
• /
• pp.591-601
• /
• 2011

In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.541-551
• /
• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.45-57
• /
• 2001

A parametric scheme is proposed for the numerical solution of the nonlinear Boussinesq equation. The numerical method is developed by approximating the time and the space partical derivatives by finite-difference re placements and the nonlinear term by an appropriate linearized scheme. The resulting finite-difference method is analyzed for local truncation error and stability. The results of a number of numerical experiments are given for both the single and the double-soliton wave. AMS Mathematics Subject Classification : 65J15, 47H17, 49D15.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.613-625
• /
• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.