• Journal of Biosystems Engineering
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• v.25 no.2
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• pp.123-130
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• 2000

A forcasting scheme for daily solar irradiance on agricultural field sis proposed by application of chaos theory to a long term observation data. It was conducted by reconstruction of phase space, attractor analysis, and Lyapunov analysis. Using the methodology , it was determined whether evolution of the five climatic data such as daily air temperature , water temperature , relative humidity, solar radiation, and wind speed are chaotic or not. The climatic data were collected for three years by an automated weather station at Hwasung-gun, Kyonggi-province. The results showed that the evolution of solar radiation was chaotic , and could be predicted. The prediction of the evolution of the solar radiation data was executed by using ' local optimal linear reconstruction ' algorithm . The RMS value of the predicting for the solar radiation evolution was 4.32 MJ/$m^2$ day. Therefore, it was feasible to predict the daily solar radiation based on the chaos theory.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.528-530
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• 1998

This paper addresses analysis and design of a fuzzy model-based-controller for the control of uncertain SISO nonlinear systems. In the design procedure, we represent the nonlinear system by using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller via parallel distributed compensation and sliding mode control. Unlike other parallel distributed controllers. this globally stable fuzzy controller is designed without finding a common positive definite matrix for a set of Lyapunov equations, and has good tracking performance. Furthermore, stability analysis is conducted not for the fuzzy model but for the real underlying nonlinear system. A simulation is included for the control of the Duffing forced-oscillation system, to show the effectiveness and feasibility of the proposed fuzzy control method.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.4
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• pp.183-190
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• 2000

It is well-known that the poles of a system are closely related with the dynamics of the systems, and the pole assignment problem, which locates the poles in the desired regions, in one of the major problem in control theory. Also, it is always possible to assign poles to specific points for exactly known linear systems. But, it is impossible for the uncertain linear systems because of the uncertainties that originate from modeling error, system variations, sensing error and disturbances, so we must consider some regions instead of points. In this paper, we consider both the analysis and the design of robust pole assignment problem of linear system with time-varying uncertainty. The considered uncertainties are the unstructured uncertainty and the structured uncertainty, and the considered region is the circular region. Based on Lyapunov stability theorem and linear matrix inequality(LMI), we first present the analysis result for robust pole assignment, and then we present the design result for robust pole assignment. Finally, we give some numerical examples to show the applicability and usefulness of our presented results.

• Proceedings of the ESK Conference
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• 1996.04a
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• pp.160-167
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• 1996

The early diagnosis has an very important role in curing dementia. But there was not an effective method to diagnose it until now. In this paper we analyzed the EEG in Alzheimer's disease and normal control groups to compare by nonlinear parameter such as the largest Lyapunov exponent $L_{1}$. We found that patients with Alzheimer's disease have significantly lower$L_{1}$ than normal groups. And we propose the nonlinear analysis of EEG as a useful tool for the early diagnosis of Alzheimer's disease.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.185-189
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• 1998

This paper addresses analysis and design of a fuzzy model-based-controller for the control of uncertain SISO nonlinear systems. In the design procedure, we represent the nonlinear system by using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller via parallel distributed compensation and sliding mode control. Unlike other parallel distributed controllers, this globally stable fuzzy controller is designed without finding a common positive definite matrix for a set of Lyapunov equations, and has good tracking performance. The stability analysis is conducted not for the fuzzy model but for the real underlying nonlinear system. Furthermore, the proposed method can be applied to partially known uncertain nonlinear systems. A numerical simulation is performed for the control of an inverted pendulum, to show the effectiveness and feasibility of the proposed fuzzy control method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.1-11
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• 1988

In this paper, the boundedness of adjustable parameters for the model reference adaptive control(MRAC) system using a constant reference signal is discussed. This analysis is motivated by that it is possibel to verify the existence, boundedness and bounded range of the parameter as well as the stability of the adaptive system with an alternative propoerty of Lyapunov function. For two adaptive laws; a general gradient mothod(GGM) and a least square method(LSM), unique solution set in parameter space can be estabilished by a new approach suggeste here. Computer simulation results to show the effect of parameter space analysis are also examined.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1821-1826
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• 2009

An adaptive neural controller for perturbed strict-feedback nonlinear system is proposed. All the previous adaptive neural (or fuzzy) controllers are based on the backstepping scheme where the universal approximators are employed in every design steps. These schemes involve virtual controls and their time derivatives that make the stability analysis and implementation of the controller very complex. This fact is called 'explosion of complexty ' since the complexity grows exponentially as the system dynamic order increases. The proposed adaptive neural control scheme adopt the backstepping design procedure only for determining ideal control law and employ only one neural network to approximate the finally selected ideal controller, which makes the controller design procedure and stability analysis considerably simple compared to the previously proposed controllers. It is shown that all the time-varing signals containing tracking error are stable in the Lyapunov viewpoint.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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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.

• Journal of applied mathematics & informatics
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• v.41 no.1
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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.

• Journal of Power Electronics
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• v.19 no.6
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• pp.1505-1514
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• 2019

The permanent magnet synchronous motor (PMSM) is widely used in various fields and the proportional-integral (PI) controller is popular in PMSM control systems. However, the motor parameters are usually unknown, which can lead to a complicated PI controller design and poor performance. In order to design a PI controller with good performance when the motor parameters are unknown, a control algorithm based on stability margin is proposed in this paper. First of all, based on the mathematical model of the PMSM and the least squares (LS) method, motor parameters are estimated offline. Then based on the estimation values of the motor parameters, natural angular frequency and phase margin, a PI controller is designed. Performance indices including the natural angular frequency and the phase margin are used directly to design the PI controller in this paper. Scalar functions of the d-loop and the q-loop are selected. It can be seen that the designed controller parameters satisfy Lyapunov large scale asymptotic stability theory if the natural angular frequencies of the d-loop and the q-loop are large than 0. Experimental results show that the parameter estimation method has good accuracy and the designed PI controller proposed in this paper has good static and dynamic performances.