• 대한수학회논문집
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• 제17권4호
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• pp.593-606
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• 2002

We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.425-430
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• 2010

In this work, We consider an initial boundary value problem for a class of nonlinear hyperbolic equations. We establish a blow-up result for certain solutions with a dissipative term.

• 제어로봇시스템학회논문지
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• 제18권7호
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• pp.613-616
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• 2012

This paper proposes the state observer design for nonlinear systems with delayed output. It is shown that by considering a nonlinear term of error dynamics as an additional state variable, the nonlinear error dynamics with time delay can be transformed into the linear one with time delay. Sufficient conditions for existence of a state observer are characterized by linear matrix inequalities. Finally, an illustrative example is given in order to show the effectiveness of our design method.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.521-536
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• 2015

We investigate the nonlinear motions of discrete loaded cable with different periodic forcing. We present the numerical evidence of the nonlinear motions of the cable by solving initial value problems and obtaining the motions after a long time. There appeared to be various types of nonlinear oscillations over a wide range of frequencies and amplitudes for the periodic forcing term.

• 대한수학회논문집
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• 제12권2호
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• pp.467-478
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• 1997

A nonlinear Galerkin method for the Burgers equation is considered. Due to the lack of the divergence free condition, the nonlinear term is treated differently compared to that of the Navier-Stokes equations. Strong convergence results are proved for the nonlinear Galerkin method.

• 대한기계학회논문집A
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• 제24권4호
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• pp.1065-1074
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• 2000

A robust nonlinear $H_2$/$H_{\infty}$ control method for a parallel inverted pendulum with structured perturbation and dry friction is proposed. By the random input describing function techniques, the nonlinear dry friction is approximated into the quasi-linear system. Introducing the quadratic robustness theorem, the robust $H_2$/$H_{\infty}$ control system is constructed for the quasi-linear perturbed system. But it is difficult to design a controller due to the nonlinear correction term in Riccati equation. With some transformations on the Riccati equation containing nonlinear correction term, the design of the robust nonlinear controller can be done easily. Hence when the stiffness and mass of the parallel inverted pendulum vary in certain ranges, the proposed control scheme has the robustness for both the structured perturbation and dry friction. The results of computer simulation show the effectiveness of our proposed control method.

• 한국정밀공학회지
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• 제15권12호
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• pp.128-141
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• 1998

We propose the robust nonlinear controller design methodology for the multivariable system which has hard nonlinearities (Coulomb friction, dead-zone, etc) and the structured real parameter uncertainty. The hard nonlinearity can be linearized by the RIDF technique and structured real parameter uncertainty can be modelled as the sense of Peterson-Hollot's quadratic Lyapunov bound. For this system, we apply the robust QLQG/H$_{\infty}$ control and then can obtain four Riccati equations. Because of the system's nonlinearity, however, one Riccati equation contains the nonlinear correction term that is very difficult to solve numerically, In order to treat this problem, using some transformations to Riccati equations, the nonlinear correction term can be eliminated. Then, only two Riccati equations need to design a controller. Finally, the robust nonlinear controller is synthesized via IRIDF techniques. To test this proposed control method, we consider the direct-drive robot manipulator system that has Coulomb frictions and varying inertia.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.125-138
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• 2003

Some Riccati type difference inequalities are established for the second-order nonlinear difference equations with negative neutral term $\Delta$(a(n)$\Delta$(x(n) - px(n-$\tau$))) + f(n, x($\sigma$(n))) = 0 using these inequalities we obtain some oscillation criteria for the above equation.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.469-481
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• 2020

In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 가을 학술발표회 논문집
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• pp.197-202
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• 2001

It is necessary to Investigate long-term behavior of vertical members such as column and shear wall because the long-term behavior induces the serviceability problem of reinforce-concrete structures. However, the long-term behavior on shear wall has not been fully studied. Experimental works are performed to understand the time dependent behavior of shear wall, especially the effect of loading area in this research. Three different types of cross sections are adopted, i.e., 10$\times$10 cm, 10$\times$30 cm, and 10$\times$50 cm with the same loading area of 10$\times$10 cm. The creep strains were different from point to point in the section of the shear wall specimen because of the nonlinear stress distribution. The effect of the nonlinear stress distribution was larger in the specimen with the larger width.