• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.6
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• pp.942-947
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• 1987

In this paper, we suggest a new adaptive control theory for discrete-time single-input single output systems based on the Lyapunov's stability theory by using the fact that the transfer function of the model is strictly positive real. And also, obervers are used in the structure of controller. The result of computer simulation shows that the proposed algorithm can be applied to both stable and unstable plants.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.195-198
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• 1995

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is the most well-known and provides precise and rigorous theoretical backgrounds. However, tile conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, it is required to consider the damping effects. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. This method tan be utilized as a powerful tool to determine the region of attraction.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.12
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• pp.983-994
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• 1989

This paper presents a new variable structure model following control algorithm for control of manipulators. The reference model is a simple double integrators and the acceleration input for the robot manipulator consists of a proportional and derivative controller for the purpose of trajectory tracking. The control algorithm is derived by using Lyapunov stability theory instead of S.S < O, as is usual in the current VSS controller design. This proposed control algorithm does not require good knowledge of the parameter in the inertia matrix and is easily extendable to robot manipulators with a higher number of links. Also, the new algorithm is computationally fast because of not requiring the matrix inversion. The computer simulation was carried out to evaluate the performance of the proposed VSMFC.

• Journal of Advanced Marine Engineering and Technology
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• v.39 no.2
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• pp.159-165
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• 2015

Motion control schemes are generally classified into three categories (point stabilization, trajectory tracking, and path following). This paper deals with the problem which is associated with the initial deployment of a group of Unmanned Surface Vehicle (USVs) and corresponding point stabilization. To keep the formation of a group of USVs, it is necessary to set the relationship between each vehicle. A forcing functions such as potential fields are designed to keep the formation and a graph Laplacian is used to represent the connectivity between vehicle. In case of fixed topology of the graph representing the communication between the vehicles, the graph Laplacian is assumed constant. However the graph topologies are allowed to change as the vehicles move, and the system dynamics become discontinuous in nature because the graph Laplacian changes as time passes. To check the stability in the stage of deployment, the system is modeled with Kronecker algebra notation. Filippov's calculus of differential equations with discontinuous right hand sides is then used to formally characterize the behavior of USVs. The stability of the system is analyzed with Lyapunov's stability theory and LaSalle's invariance principle, and the validity is shown by checking the variation of state norm.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.341-344
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• 2007

This paper proposes an alternative robust adaptive high-gain fuzzy observer design scheme and its application to synchronization of chaotic systems. The structure of the proposed observer is represented by Takagi-Sugeno fuzzy model and has the integrator of the estimation error. This improves the performance of high-gain observer and makes the proposed observer robust against noisy measurements, uncertainties and parameter perturbations as well. Using Lyapunov stability theory, an adaptive law is derived and the stability of the proposed observer is analyzed. Some simulation result is given to present the validity of theoretical derivations and the performance of the proposed observer.

• Journal of Astronomy and Space Sciences
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• v.29 no.4
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• pp.389-395
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• 2012

The problem of spacecraft attitude control is solved using an adaptive neuro-fuzzy inference system (ANFIS). An ANFIS produces a control signal for one of the three axes of a spacecraft's body frame, so in total three ANFISs are constructed for 3-axis attitude control. The fuzzy inference system of the ANFIS is initialized using a subtractive clustering method. The ANFIS is trained by a hybrid learning algorithm using the data obtained from attitude control simulations using state-dependent Riccati equation controller. The training data set for each axis is composed of state errors for 3 axes (roll, pitch, and yaw) and a control signal for one of the 3 axes. The stability region of the ANFIS controller is estimated numerically based on Lyapunov stability theory using a numerical method to calculate Jacobian matrix. To measure the performance of the ANFIS controller, root mean square error and correlation factor are used as performance indicators. The performance is tested on two ANFIS controllers trained in different conditions. The test results show that the performance indicators are proper in the sense that the ANFIS controller with the larger stability region provides better performance according to the performance indicators.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.317-335
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• 2014

In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters $R_0$ (the basic infection reproduction number) and $R_1$ (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle's invariance principle.

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

• Steel and Composite Structures
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• v.46 no.1
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• pp.107-114
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• 2023

A new intelligent adaptive control scheme was proposed that combines observer disturbance-based adaptive control and fuzzy adaptive control for a composite structure with a mass-adjustable damper. The most important advantage is that the control structures do not need to know the uncertainty limits and the interference effect is eliminated. Three adjustable parameters in LMI are used to control the gain of the 2D fuzzy control. Binary performance indices with weighted matrices are constructed to separately evaluate validation and training performance using the revalidation learning function. Determining the appropriate weight matrix balances control and learning efficiency and prevents large gains in control. It is proved that the stability of the control system can be ensured by a linear matrix theory of equality based on Lyapunov's theory. Simulation results show that the multilevel simulation approach combines accuracy with high computational efficiency. The M-TMD system, by slightly reducing critical joint load amplitudes, can significantly improve the overall response of an uncontrolled structure.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.760-765
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• 1992

In this paper, robust adaptive control algorithms which can be applied to unknown uncertain systems are suggested. Transform matrix for dividing states into "uncontrolled" states and "controlled" states and general searching procedure for the transform matrix which assign arbitrary n-1 eigen values for the uncontrolled subsystem of n-th order single-input single-output systems is also studied and utilized for the design of new-type controllers. We derived new-type control laws by using adaptive control theory and variable structure system and its stability is proved by using Lyapunov stability theory. From computer simulation results, we can see that the proposed adaptive control algorithm is robust and stable.s robust and stable.