• Journal of Electrical Engineering and Technology
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• v.10 no.1
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• pp.408-421
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• 2015

Because the wheel of V-belt continuously variable transmission (CVT) system driven by permanent magnet synchronous motor (PMSM) has much unknown nonlinear and time-varying characteristics, the better control performance design for the linear control design is a time consuming job. In order to overcome difficulties for design of the linear controllers, a hybrid recurrent Chebyshev neural network (NN) control system is proposed to control for a PMSM servo-driven V-belt CVT system under the occurrence of the lumped nonlinear load disturbances. The hybrid recurrent Chebyshev NN control system consists of an inspector control, a recurrent Chebyshev NN control with adaptive law and a recouped control. Moreover, the online parameters tuning methodology of adaptive law in the recurrent Chebyshev NN can be derived according to the Lyapunov stability theorem and the gradient descent method. Furthermore, the optimal learning rate of the parameters based on discrete-type Lyapunov function is derived to achieve fast convergence. The recurrent Chebyshev NN with fast convergence has the online learning ability to respond to the system's nonlinear and time-varying behaviors. Finally, to show the effectiveness of the proposed control scheme, comparative studies are demonstrated by experimental results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.9
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• pp.859-866
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• 2008

A guidance scheme for controlling the relative geometry of multiple flight vehicle formation flying is proposed. Each flight vehicle in the formation takes the roles of leader and follower simultaneously except for the formation leader. In this scheme, the flight commands for a leader are shared by all the followers and this leaders to a synchronized flight of all flight vehicles comprising the formation. Lyapunov stability theorem is used to obtain the guidance law. High fidelity nonlinear simulation results are presented to show the effectiveness of the proposed guidance law using a reconnaissance and surveillance mission example.

• 전자공학회논문지 IE
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• v.46 no.4
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• pp.49-56
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• 2009

In this paper, stabilization inverse optimal control for nonlinear systems with structural uncertainty is considered. Based on the control Lyapunov function, a theorem for the globally asymptotic stability is presented. From this a less conservative condition for the inverse optimal control is derived. The result is used to design an inverse optimal controller for a class of nonlinear systems, that improves and extends the existing results. The class of nonlinear system considered is also enlarger. The simulation results show the effectiveness of the method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.5
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• pp.41-47
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• 2002

In this paper, a guidance law applicable to aircraft automatic landing is proposed and its performance is compared with the conventional ILS-type landing approach. The concept of miss distance, which is commonly used in the missile guidance laws, and Lyapunov stability are effectively combined to obtain the landing guidance law. The new landing guidance law is integrated into the existing controller and is applied to the landing approach and flare phases of landing procedure. Numerical simulation results show that the new landing guidance law is a viable alternative to the conventional strategies that directly control the longitudinal deviation or altitude.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.953-955
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• 1993

In this paper we propose a new stability theorem and a robust stability condition for linguistic fuzzy model systems in state space. First we define a stability in linear sense. After representing the fuzzy model by a system with disturbances, A necessary and sufficient condition for the stability is derived. This condition is proved to be a sufficient condition of the fuzzy model. The Q in the Lyapunov equation is iteratively adjusted by an gradient-based algorithm to improve its stability test. Finally, stability robustness bounds of a system having modeling error is derived. An example is also included to show that the stability test is powerful.

• The Transactions of the Korean Institute of Power Electronics
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• v.4 no.2
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• pp.138-143
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• 1999

A new control method for the precision robust position control of a brushless DC(BLDC) motor for direct drive m motor(BLDDM) system using the asymptotically stable adaptive load torque observer is presented. A precision position c control is obtained for the BLDD motor system appro성mately linearized using the fieldlongrightarroworientation method. Many of t these motor systems have BLDD motor to obtain no backlashes. On the other hand, it has disadvantages such as the h high cost and more complex controller caused by the nonlinear characteristics. And the load torque disturbance is d directly affected to a motor shaft. To r밍ect this problem, stability analysis is calTied out using Lyapunov stability t theorem. Using this results, the stability is proved and load disturbance detected by the asymptotically stable adaptive observer is compensated by feedforwarding the equivalent CUlTent having the fast response.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1097-1115
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• 2011

We consider the global stability of a general tuberculosis model with two differential infectivity, n classes of latent individuals and mass action incidence. This system exhibits the traditional threshold behavior. There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction ratio $\mathcal{R}_0$, this state can be either endemic ($\mathcal{R}_0$ > 1), or infection-free ($\mathcal{R}_0{\leq}1$). The global stability of this model is derived through the use of Lyapunov stability theory and LaSalle's invariant set theorem. Both the analytical results and numerical simulations suggest that patients should be strongly encouraged to complete their treatment and sputum examination.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1267-1271
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• 2003

This paper proposes an indirect adaptive fuzzy controller for general SISO nonlinear systems. No a priori information on bounding constants of uncertainties including reconstruction errors and optimal fuzzy parameters is needed. The control law and the update laws for fuzzy rule structure and estimates of fuzzy parameters and bounding constants are determined so that the Lyapunov stability of the whole closed loop system is guaranteed. The computer simulation results for an inverted pendulum system show the performance of the proposed robust adaptive fuzzy controller.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.491-493
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• 1999

In this paper, we consider the design of robust pole assignment for linear system. Considered uncertainty is time-varying uncertainty. Based on Lyapunov stability theorem and linear matrix inequality(LMI) we present the design result for pole assignment. Finally, we give some numerical examples to show the applicability and usefulness of our presented results.