• Proceedings of the KIEE Conference
• /
• 2003.07d
• /
• pp.2190-2192
• /
• 2003

In this paper, a state observer based direct adaptive fuzzy controller for unknown nonlinear dynamical system is presented. The adaptive parameters of the direct adaptive fuzzy controller can be tuned by using a projection algorithm on-line based on the Lyapunov synthesis approach. A maximum control is used to guarantee the robustness of system. A stability analysis of the overall adaptive scheme is discussed based on the sense of Lyapunov. The inverted pendulum simulation example shows that proposed control algorithm can be used for the tracking problem of nonlinear system.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.3
• /
• pp.1232-1240
• /
• 2018

This paper aims at designing an intelligent controller, based on control Lyapunov Function strategy integrated with fabricating discrete model of Buck and Boost converters and analyzing energy changes during the DC/DC progress to realize tracing reference current on Buck and Boost converters. In addition, practical stability phenomenon research and transient performance analysis has been proposed to give an insight to the influence of controller parameters in achieving an enhanced output performance and how the time of sample period affect the error of practical stability will be illustrated. The novelty of this controller in comparison to other schemes lies in the improved performance of practical stability.

• Journal of Power Electronics
• /
• v.17 no.6
• /
• pp.1611-1624
• /
• 2017

With the rapid development of microgrid technology, microgrid projects are no longer limited to laboratory demonstrations and pilot platforms. It shows greater value in practical applications. Hence, the smooth interaction between a microgrid and the main grid plays a critical role. In this paper, a control method based on active disturbance rejection control (ADRC) is proposed in order to realize seamless transitions between grid-connected and islanding operation modes and stable operation with variable loads. It is verified by simulations that the proposed ADRC-based method features better performance when compared to conventional proportional-integral-differential (PID) control. Meanwhile, the stability of the third-order extended state observer (ESO) in second-order ADRC is validated by using Lyapunov stability criteria.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.21 no.6
• /
• pp.850-856
• /
• 2018

In this paper, a controller based on repetitive learning control is designed to control an unmanned surface vessel with nonlinear characteristics and unknown parameters. First, we define the equations of motion and error system of the unmanned vessel, and then design an repetitive learning controller composed of system error and estimated unknown parameters based on repetitive learning control and adaptive control. The stability of the unmanned vessel model controlled by the designed controller is verified through the analysis of the Lyapunov stability. Simulation shows that the error converges asymptotically to zero with semi-global result, confirming that the unmanned vessel is moving toward a given ideal path, and verifies that the controller is also feasible.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.1
• /
• pp.39-63
• /
• 2019

In this paper, we study the effect of Cytotoxic T Lymphocyte (CTL) and antibody immune responses on the virus dynamics with both virus-to-cell and cell-to-cell transmissions. The infection rate is given by Holling type-II. We first show that the model is biologically acceptable by showing that the solutions of the model are nonnegative and bounded. We find the equilibria of the model and investigate their global stability analysis. We derive five threshold parameters which fully determine the existence and stability of the five equilibria of the model. The global stability of all equilibria of the model is proven using Lyapunov method and applying LaSalle's invariance principle. To support our theoretical results we have performed some numerical simulations for the model. The results show the CTL and antibody immune response can control the disease progression.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.669-688
• /
• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.402-418
• /
• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• Advances in nano research
• /
• v.15 no.1
• /
• pp.25-34
• /
• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• Journal of Industrial Technology
• /
• v.10
• /
• pp.3-8
• /
• 1990

This paper presents a linear state feedback control approach to the stabilization of discrete-time uncertain systems with bounded uncertain parameters. The approach is based on the LQ(linear quadratic) regulator theory and Lyapunov's stability analysis. Asymptotically stable behavior is guaranteed in the presence of parameter uncertainties, and the upper bound of the performance index is determined.

• Computers and Concrete
• /
• v.30 no.4
• /
• pp.237-242
• /
• 2022

This paper is concerned with exponential stability in mean square for stochastic static neutral neural networks with varying delays. By using Lyapunov functional method and with the help of stochastic analysis technique, the sufficient conditions to guarantee the exponential stability in mean square for the neural networks are obtained and some results of related literature are extended.