• 동력기계공학회지
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• 제21권4호
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• pp.42-50
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• 2017

A velocity controller using a modified model reference adaptive controller (M-MRAC) and a projection operator for a fish sorting belt conveyor system with uncertainty parameters, input saturation and bounded disturbances is proposed in this paper. To improve the tracking performance and robustness of the proposed controller in the presence of bounded disturbances, the followings are done. Firstly, the reference model for the conventional model reference adaptive controller (CMRAC) is replaced by a modified reference model for a M-MRAC to reduce unexpected high frequency oscillation in control input signal when the adaptation rate is increased. Secondly, estimated parameters in an adaptive law are varied smoothly under bounded external disturbances and a projection operator is utilized in an adaptive law for the proposed M-MRAC controller to be robust. Thirdly, an auxiliary error vector is introduced for compensating the error dynamics of the system when the saturation input occurs. Finally, the experimental results are shown to verify the better effectiveness and performance of the proposed controller under the bounded disturbance and saturated input than that of a CMRAC.

• Coupled systems mechanics
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• 제7권6호
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• 대한수학회보
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• 제44권3호
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• pp.507-516
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• 2007

Let M be a complete Riemannian manifold and L be a $Schr\"{o}dinger$ operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on the L-nonparabolic end, which vanish at the boundary of the end.

• 제어로봇시스템학회논문지
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• 제11권6호
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• pp.492-495
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• 2005

This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded control. Using linear matrix inequalities(LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We show that our estimate is always better than the estimate of [3].

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.337-343
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• 2006

In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ${\omega}$, the pointwise convergence and the uniform convergence of a sequence of ${\omega}$-bounded exponentially convex functions on S which are also continuous at the identity are equivalent.

• 대한수학회보
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• 제52권1호
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• pp.173-182
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• 2015

In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p < $1+\frac{4}{N-1}$ for $N{\geq}2$ or 1 < p < 5 for N = 1.

• 대한수학회보
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• 제52권1호
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• pp.69-83
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• 2015

In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.

• 대한수학회보
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• 제52권1호
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• pp.45-56
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• 2015

In this paper, we study the relation between two dynamical systems (V, f) and (V, g) with $f{\circ}g=g{\circ}f$. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Preper(f)) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f.

• 대한수학회보
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• 제55권6호
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• pp.1703-1711
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• 2018

The main aim of this paper is to study the fourth Hankel determinant for the class of functions with bounded turning. We also investigate for 2-fold symmetric and 3-fold symmetric functions.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.