• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 제38회 하계학술대회
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• pp.1730-1731
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• 2007

In this paper, we present a direct adaptive control method using neural networks for the control of nonlinear systems. The weights of neural networks are trained by an adaptive backpropagation algorithm based on Lyapunov stability theory. We develop the parameter update-laws using the neural network input and the error between the desired output and the output of nonlinear plant to update the weights of a neural network in the sense that Lyapunove stability theory. Beside the output tracking error is asymptotically converged to zero.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 제38회 하계학술대회
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• pp.1644-1645
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• 2007

This paper proposes an adaptive sliding mode control method for trajectory tracking of nonholonomic mobile robots with model uncertainties and external disturbances. The kinematic model represented by polar coordinates are considered to design a robust control system. Wavelet neural networks (WNNs) are employed to approximate arbitrary model uncertainties in dynamics of the mobile robot. From the Lyapunov stability theory, we derive tuning algorithms for all weights of WNNs and prove that all signals of an adaptive closed-loop system are uniformly ultimately bounded.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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• pp.2320-2322
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• 2001

This paper describes the design of a robust adaptive neural-net(NN) observer for uncertain nonlinear dynamical system. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property of the state estimation error, as well as of all other signals in the closed-loop system. Especially, for reducing the dynamic oder of the observer, we propose a new method in which no strictly positive real(SPR) condition is needed with on-line estimation of weights of the NNs. No a priori knowledge of an upper bounds on the uncertain terms is required. The theoretical results are illustrated through a simulation example.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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• pp.1955-1957
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• 2001

This paper propose the design method of robust tracking controller for nonlinear TS fuzzy system with uncertainties. The robust tracking controller design is presented by constraint of robust stability for nonlinear system. A sufficient condition of the robust stability is presented by LMI(Linear Matrix Inequality) soltuion in the sense of Lyapunov for TS fuzzy system with uncertainties. The effectiveness of the proposed robust tracking con design is demonstrated through a numerical simulatio.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권2호
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• pp.77-83
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• 2011

In this paper, an active backstepping design is proposed to achieve control and synchronization of a new hyperchaotic system. The proposed method is a systematic design approach and exists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of the active control. The proposed controller enables stabilization of chaotic motion to the origin as well as synchronization of the two identical new hyperchaotic systems. Numerical simulations illustrate the validity of the proposed control technique.

• 산업경영시스템학회지
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• 제19권39호
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• pp.129-142
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• 1996

The early diagnosis has an very important role in curing dementia. But there was not the effective method to diagnose it until now. In this paper we analyzed the EEG of Alzheimer's disease patients and normal groups by nonlinear methods. In the analysis we calculated the correlation dimensions $D_2$ and the largest Lyapunov exponent $L_1$. We found that patients with Alzheimer's disease have significantly lower $D_2$ and TEX>$L_1$ than normal groups. It means that brains injured by Alzheimer's disease have electrophysiological inactive elements and have decreased chaotic behaviour. We propose the nonlinear analysis of the EEG as a useful tool for the early diagnosis of Alzheimer's disease.

• 대한임베디드공학회논문지
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• 제14권5호
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• pp.269-275
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• 2019

This paper addresses the control problem of cyber-physical systems under controller attack. A novel discontinuous Lyapunov functionals are employed to fully utilize sampled-data pattern which characteristic is commonly appeared in cyber-physical systems. By considering the limited resource of networks, cyber-attacks on the controller are considered randomly occurring and are described as an attack function which is nonlinear but assumed to be satisfying Lipschitz condition. Novel criteria for designing controller with robustness for cyber-attacks are developed in terms of linear matrix inequality (LMI). Finally, a numerical example is given to prove the usefulness of the proposed method.

• 대한수학회지
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• 제58권1호
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• pp.45-67
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• 2021

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.859-888
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• 2021

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.