• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.69-72
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• 1987

General schemes for the adaptive control and identification of multivariable systems by model reference approach are developed. Lyapunov's direct method and LaSalle's theorem are employed to ensure the stability of these schemes. An added feature is the simplicity of the stable adaptive laws, which depend explicitly on the state variables of plant and model, and on the plant input. Computer simulation results of several examples illustrate the the effectiveness of the proposed schemes.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.1
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• pp.38-44
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• 2001

This paper investigates the direct adaptive control of nonlinear systems using RBFN(radial basis function networks). The structure of the controller consists of a fixed PD controller and a RBFN controller in parallel. An adaptation law for the parameters of RBFN is developed based on the Lyapunov stability theory to guarantee the stability of the overall control system. The filtered tracking error between the system output and the desired output is shown to be UUB(uniformly ultimately bounded). To evaluate the performance of the controller, the proposed method is applied to the trajectory contro of the two-link manipulator.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2992-2994
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• 1999

This paper investigates the direct adaptive control of nonlinear systems using RBFN(radial basis function networks). The structure of the controller consists of a fixed PD controller and a RBFN controller in parallel. An adaptation law for the weight adjustment is developed based on the Lyapunov stability theory to guarantee the stability of the overall control scheme. Also, the tracking errors between the system outputs and the desired outputs converge to zero asymptotically. To evaluate the performance of the controller, the proposed method is applied to the trajectory control of the two-link manipulator.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.107-121
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• 2023

An epidemic infectious disease model consists of six compartments viz. Susceptible, Exposed, Infected, Quarantine, Recovered, and Virus with nonlinear saturation incidence rate is proposed to know the viral disease dynamics. There exist two biological equilibrium points for the model system. The system's local and global stability is done through Lyapunov's direct method about equilibrium points. The sensitivity analysis has been performed for the basic reproduction number and equilibrium points through the normalized forward sensitivity index. Sensitivity analysis shows that virus growth and quarantine rates are more sensitive parameters. In support of mathematical conclusions, numerical experimentation has been shown.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.5
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• pp.452-461
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• 2007

Adaptive anti-sway and trajectory tracking control of overhead crane is presented, which utilizes Fuzzy Uncertainty Observer(FUO) and Fuzzy based Variable Structure Control(FVSC). We consider an overhead crane system which can be decoupled into the actuated and unactuated subsystems with its own lumped uncertainty such as parameter uncertainties and external disturbance. First, a new method for anti-sway control using FVSC is proposed to improve the conventional method based on Lyapunov direct method, while a conventional trajectory tracking control law using feedback linearization is directly adopted. Second, FUO is designed to estimate one of the two lumped uncertainties which can compensate both of them, based on the fact that two lumped uncertainties are coupled with each other. Then, an adaptive anti-sway control is proposed by incorporating the proposed FVSC and FUO. Under the condition that the observation error is Uniformly Ultimately Bounded(UUB) within an arbitrarily shrinkable region, the overall closed-loop system is shown to be Globally Uniformly Ultimately Bounded(GUUB). In addition, the Global Asymptotic Stability(GAS) of it is shown under the vanishing disturbance assumption. Finally, the effectiveness of the proposed scheme has been confirmed by numerical simulations.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.898-901
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• 1988

Up to now, using adaptive control method, Identification deals with system whose entire state variables and prameters are accessible for measurement. In practical situations, all the state variables cannot be measured and it is impossible to directly apply since the parameters of the system are unknown. Therefore, in this paper, using only input-output data, such a model of the system is not available since the parameters of the system are unknown. this leads to the concept of an adptive observer in which both the parameters and the state variable of the system are identified simultaniously. Lyapunov's direct method and Kalman-Yakubovich (K-Y) lemma are employed to ensure the stability of this schemes. The feature is that the signal and adaptive gain which is generated from filter is imposed upon feedback vector and then state variables and the unknown parameters can be identified. To show the usefulness of the proposed schemes, computer simulation result of unknown second-order system shows the effectiveness of the proposed schems.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.531-536
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• 2003

In this paper, a redesigned guidance and control system for a lunar lander is presented. In past studies, the authors developed a trajectory and attitude control system which achieves the vertical soft landing on the lunar surface. It is confirmed that the system has a good tracking ability to a predefined profile and good robustness against a thruster failure mode where a partial failure of clustered engines was assumed. However, under the previous control laws, the landing point tends to be shifted, in response to the system parameter values, from a target point. Also, an unbalanced moment due to a thruster failure mode was not considered in the simulation. Therefore, in this study, the downrange control is added to the system to enable the vehicle to land at a pre-assigned target point accurately. Furthermore, inhibiting the effect of the unbalanced moment is attempted thorough redesigning the attitude control system. A numerical simulation was performed to confirm the ability of the proposed system with regard to the above problems. Moreover, in the past simulations, a low initial altitude was assumed as an initial condition: in this study, however, the performance of the proposed system is examined over the whole trajectory from an initial altitude of 10 [km] to the lunar surface.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.12
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• pp.128-141
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• 1998

We propose the robust nonlinear controller design methodology for the multivariable system which has hard nonlinearities (Coulomb friction, dead-zone, etc) and the structured real parameter uncertainty. The hard nonlinearity can be linearized by the RIDF technique and structured real parameter uncertainty can be modelled as the sense of Peterson-Hollot's quadratic Lyapunov bound. For this system, we apply the robust QLQG/H$_{\infty}$ control and then can obtain four Riccati equations. Because of the system's nonlinearity, however, one Riccati equation contains the nonlinear correction term that is very difficult to solve numerically, In order to treat this problem, using some transformations to Riccati equations, the nonlinear correction term can be eliminated. Then, only two Riccati equations need to design a controller. Finally, the robust nonlinear controller is synthesized via IRIDF techniques. To test this proposed control method, we consider the direct-drive robot manipulator system that has Coulomb frictions and varying inertia.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.6
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• pp.142-155
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• 2000

A MIMO model reference control scheme incorporating the variable structure theory for a vehicle four wheel steering system(4WS) is proposed and evaluated for a class of continuous-time nonlinear dynamics with known or unknown uncertainties. The scheme employs an neural network to identify the plant systems, where the neural network estimates the nonlinear dynamics of the plant. By the Lyapunov direct method, the algorithm is proven to be globally stable, with tracking errors converging to the neighborhood of zero. The merits of this scheme is that the global system stability is guaranteed and it is not necessary to know the exact structure of the system. With the resulting identification model which contains the neural networks, it does not need higher degrees of freedom vehicle model than 3 degree of freedom model. Th proposed scheme is applied to the active four wheel system and shows the validity is used to investigate vehicle handing performances. In simulation of the J-turn maneuver, the reduction of yaw rate overshoot of a typical mid-size car improved by 30% compared to a two wheel steering system(2WS) case, resulting that the proposed scheme gives faster yaw rate response and smaller side angle than the 2WS case.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.37 no.1
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• pp.21-31
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• 2000

In this paper, an analysis of the stability for a class of discrete-time neural network control systems is presentd. Based on Lyapunov's direct method, a sufficient stability condition for the neural network control systems is systematically derived and the modified back propagation algorithm which reflects the derived stability condition is suggested. The modified BP originates from the derived sufficient condition and guarantees the exponential stability of the resulting trained closed system. Finally, computer simulation is included to show an example where the derived stability condition and the BP modified bythe condition is used to train the control plant.