• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.137-170
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• 2015

In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.3
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• pp.256-263
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• 2013

The saturation of the actuator impairs the response performance of the near space interceptor control system. A control system based on the properties of linear tracking system is designed for this problem. The properties are that the maximum value of the pseudo-Lyapunov function of the linear tracking control system do not present at the initial state but at the steady state, based on which the bounded stability problem is converted into linear tracking problem. The pseudo-Lyapunov function of the linear tracking system contain the input variables; the amplitude and frequency of the input variables affect the stability of the nonlinear control system. Designate expected closed-loop poles area for different input commands and obtain a controller which is function of input variables. The coupling between variables and linear matrices make the control system design problem non-convex. The non-convex problem is converted into a convex LMI according to the Shur complement lemma and iterative algorithm. Finally the simulation shows that the designed optimal control system is quick and accurate; the rationality of the presented design techniques is validated.

• International Journal of Control, Automation, and Systems
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• v.5 no.3
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• pp.283-294
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• 2007

In this paper, a nonlinear controller based on adaptive sliding-mode method which has a sliding surface vector including new boundizing function is proposed and applied to a two-wheeled welding mobile robot (WMR). This controller makes the welding point of WMR achieve tracking a reference point which is moving on a smooth curved welding path with a desired constant velocity. The mobile robot is considered in view of a kinematic model and a dynamic model in Cartesian coordinates. The proposed controller can overcome uncertainties and external disturbances by adaptive sliding-mode technique. To design the controller, the tracking error vector is defined, and then the sliding surface vector including new boundizing function and the adaptation laws are chosen to guarantee that the error vector converges to zero asymptotically. The stability of the dynamic system is shown through the Lyapunov method. In addition, a simple way of measuring the errors by potentiometers is introduced. The simulations and experimental results are shown to prove the effectiveness of the proposed controller.

• Journal of Electrical Engineering and Technology
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• v.6 no.5
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• pp.697-705
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• 2011

In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.05a
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• pp.638-642
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• 2001

In this paper we propose a noise reduction algorithm which based on cellular automata with the local median rule. It is supposed that there is no information about the features of the image that must be improved. The proposed method behavior is to locally increase or decrease the gray level differences of the image without loss of the main characteristics of the image. The dynamical behavior of these automata is completely determined by Lyapunov operators for sequential and parallel update. We have found that the automata present very fast convergence to fixed points, stability in front of random noisy images. Based on the experimental results we discuss the advantage and efficiency.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 1997.11a
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• pp.69-74
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• 1997

Sleep deprivation may affect the brain functions such as cognition and, consequentoy, dynamics of the EEG. we examiced the effects of sleep deprivation on chaoticity of EEG. Five volunteers were sleep-deprived over a period of 24 hours, They were checked by EEG during two days, the first day of baseline period, EEGs were reorded form 16 channels for nonlinear analysis. We dmployed a method of minimum cmbedding dimension to calculate the first positive Lyapunov exponent. For limited noisy data, this algorithm was strikingly faster and more accurate than previous ones. Our results show that the sleep deprived volunteers had lower values of the first positive Lyapunov exponent at ten channels (Fp$\_$1/, F$\_$4/, F$\_$8/, T$\_$4/, T$\_$5/, C$\_$3/, C$\_$4/, P$\_$3/, p$\_$4, O$\_$1/) compared with the values of baseline periods. These results suggested that sleep deprivation leads to decreawe of chaotic activity in brain and impairment of the information processing in the brain. We suggested that nonlinear analysis of the EEG before and after sleep deprivation may offer fruitful perspectives for understanding the role o f sleep deprivation on the brain function.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.4
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• pp.343-350
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• 2004

This study is on control gain estimation of energy dissipation control algorithms. Velocity feedback saturated, bang bang, and energy gain control algorithms are proposed based on the Lyapunov stability theory and their performances are evaluated and compared. Saturation problem is considered in the design of the velocity feedback saturated and energy-gain control algorithms, and chattering problem in bang bang control is solved by using boundary layer. Numerical results show that the proposed control algorithms can dissipate the structural energy induced by wind loads efficiently.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.779-786
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• 2009

This paper deals with $H_{\infty}$ fuzzy control problem of discrete-time nonlinear Markovian jump systems with time delay. The Takgi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the Markovian jump fuzzy system with time delay. Stochastic Lyapunov function is dependent on the operation modes of the system. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller are given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficient of the proposed design methods.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.47-62
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• 1997

This paper is concerned with investigating the global as-ymptotic behavior of the zero solution of the initial-boundary value problem for a nonlinear fourth order wave equation, Moreover an esti-mate of the rate of decay of the solutions is obtained.