• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.584-596
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• 2019

This paper presents a Modified Adaptive Complementary Sliding Mode Control (MACSMC) system for the longitudinal motion control of the Fully-Submerged Hydrofoil Craft (FSHC) in the presence of time varying disturbance and uncertain perturbations. The nonlinear disturbance observer is designed with less conservatism that only boundedness of the derivative of the disturbance is required. Then, a complementary sliding mode control system combined with adaptive law is designed to reduce the bound of stabilization error with fast convergence. In particularly, the modified complementary sliding mode surface which contains the estimation of the disturbance can reduce the switching gain and retain the normal performance of the system. Moreover, a hyperbolic tangent function contained in the control law is utilized to attenuate the chattering of the actuator. The global asymptotic stability of the closed-loop system is demonstrated utilizing the Lyapunov stability theory. Ultimately, the simulation results show the effectiveness of the proposed approach.

• 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 applied mathematics & informatics
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• v.31 no.1_2
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• pp.1-25
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• 2013

In this paper we have developed a mathematical model of alcohol abuse. It consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined. Sensitivity analysis of $R_0$ identifies ${\beta}_1$, the transmission coefficient from moderate and occasional drinker to heavy drinker, as the most useful parameter to target for the reduction of $R_0$. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0$ < 1. It is found that, when $R_0$ = 1, a backward bifurcation can occur and when $R_0$ > 1, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE. Our aim of this analysis is to identify the parameters of interest for further study with a view for informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.2
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• pp.210-220
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• 2012

The model-free control of aeroelastic vibrations of a non-linear 2-D wing-flap system operating in supersonic flight speed regimes is discussed in this paper. A novel continuous robust controller design yields asymptotically stable vibration suppression in both the pitching and plunging degrees of freedom using the flap deflection as a control input. The controller also ensures that all system states remain bounded at all times during closed-loop operation. A Lyapunov method is used to obtain the global asymptotic stability result. The unsteady aerodynamic load is considered by resourcing to the non-linear Piston Theory Aerodynamics (PTA) modified to account for the effect of the flap deflection. Simulation results demonstrate the performance of the robust control strategy in suppressing dynamic aeroelastic instabilities, such as non-linear flutter and limit cycle oscillations.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.1-12
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• 2002

This paper considers the robust and optimal three-axis attitude stabilization of rigid spacecraft with inertia uncertainties. The attitude motion of rigid spacecraft described in terms of either the Cayley-Rodrigues parameters or the Modified Rodrigues parameters is considered. A class of robust nonlinear control laws with relaxed feedback gain structures is proposed for attitude stabilization of rigid spacecraft with inertia uncertainties. Global asymptotic stability of the proposed control laws is shown by using the LaSalle Invariance Principle. The optimality properties of the proposed control laws are also investigated by using the Hamilton-Jacobi theory. A numerical example is given to illustrate the theoretical results presented in this paper.

• Proceedings of the KIEE Conference
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• 1989.11a
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• pp.426-429
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• 1989

The robust self-tuning controller is designed which is guaranteed the asymptotic regulation and tracking in the presence of a bounded parameter perturbation. The global stability in the presence of a finite noise and disturbance is ensured. The controller has a error driven structure, and involves the common model of a disturbance and reference input in the internal model. The adaptive system tunes the controller parameters such that the quadratic performance index which involves a weighting factor is optimized.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.109.1-109
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• 2001

This paper deals with the path following problem of car-like intelligent mobile robot. A robust sliding mode control law based on time-varying state feedback is performed via Lyapunov method for path tracking of nonholonomic mobile robot with uncertainties. At first, A sliding control law is designed by combing the natural algebraic structure of the chained form system with ideas from sliding mode theory. Then, a robust control law is proposed to impose robustness against bounded uncertainties in path tracking. The problem of estimating the asymptotic stability region and the sliding domain of uncertain sliding mode system with bounded control input is also discussed. The proposed sliding mode control law can ensure the global reaching condition of the uncertain control system.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.721-741
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• 2011

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers, smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values $R_0$ and $R^*$ and further obtained that the smoking class in the community will be permanent when $R_0$ > 1 and the smoking class in the community will be going to extinct when $R^*$ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.598-600
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• 1998

In this paper, a robust controller is proposed to achieve the accurate tracking for uncertain robot manipulators with hydraulic actuator dynamics. The parameter uncertainty can be quantified by the linear parameterization technique. A switching controller is proposed to guarantee the global asymptotic stability of the plant. In order to eliminate the chattering caused by the switching controller, a smoothing controller is proposed using the boundary layer technique around the sliding surface. It is shown that the smoothing controller guarantees the uniform ultimate boundedness of the tracking, error. The proposed controller shows good better tracking performance.

• Journal of Power Electronics
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• v.9 no.4
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• pp.582-592
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• 2009

This paper proposes a new speed sensorless direct torque and flux controlled interior permanent magnet synchronous motor (IPMSM) drive. Closed-loop control of both the torque and stator flux linkage are achieved by using two proportional-integral (PI) controllers. The reference voltage vectors are generated by a SVM unit. The drive uses an adaptive sliding mode observer for joint stator flux and rotor speed estimation. Global asymptotic stability of the observer is achieved via Lyapunov analysis. At low speeds, the observer is combined with the high frequency signal injection technique for stable operation down to standstill. Hence, the sensorless drive is capable of exhibiting high dynamic and steady-state performances over a wide speed range. The operating range of the direct torque and flux controlled (DTFC) drive is extended into the high speed region by incorporating field weakening. Experimental results confirm the effectiveness of the proposed method.