• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1375-1382
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• 2015

We investigate what happens when we try to work with continuing block codes (i.e., left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on strictly sofic shifts do not behave as well as those on shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is always a shift of finite type.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.30 no.4
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• pp.329-340
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• 1994

This paper presents a dynamic compensation methodology for robust trajectory tracking control of uncertain robot manipulators. To improve tracking performance of the system, a full model-based feedforward compensation with continuous VS-type robust control is developed in this paper(i.e,. robust decentralized adaptive control scheme). Since possible bounds of uncertainties are unknown, the adaptive bounds of the robust control is used to directly estimate the uncertainty bounds(instead of estimating manipulator parameters as in centralized adaptive control0. The global stability and robustness issues of the proposed control algorithm have been investigated extensively and rigorously via a Lyapunov method. The presented control algorithm guarantees that all system responses are uniformly ultimately bounded. Thus, it is shown that the control system is evaluated to be highly robust with respect to significant uncertainties.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.2
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• pp.179-189
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• 2011

In this paper, robust adaptive control design problem is addressed for a class of parametrically uncertain aeroelastic systems. A full-state robust adaptive controller was designed to suppress aeroelastic vibrations of a nonlinear wing section. The design used leading and trailing edge control actuations. The full state feedback (FSFB) control yielded a global uniformly ultimately bounded result for two-axis vibration suppression. The pitching and plunging displacements were measurable; however, the pitching and plunging rates were not measurable. Thus, a high gain observer was used to modify the FSFB control design to become an output feedback (OFB) design while the stability analysis for the OFB control law was presented. Simulation results demonstrate the efficacy of the multi-input multi-output control toward suppressing aeroelastic vibrations and limit cycle oscillations occurring in pre- and post-flutter velocity regimes.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.687-690
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• 1991

In deterministic design of feedback controllers for uncertain dynamical systems, the bound on the uncertainty is an important clue to guarantee the asymptotic stability or uniform ultimate boundedness of the closed-loop system. In this paper, using only the measurable output we propose an adaptation law for the estimation of the bound of the uncertainty. And based on this adaptation law an adaptive control which renders the uncertain dynamical systems uniformly ultimately bounded is constructed.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.8
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• pp.1592-1598
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• 2011

In this paper, a formation control method based on the leader-following approach for nonholonomic mobile robots is proposed. In the previous works, it is assumed that the followers know the leader's velocity by means of communication. However, it is difficult that the followers correctly know the leader's velocity due to the contamination or delay of information. Thus, in this paper, an adaptive approach based on the parameter projection algorithm is proposed to estimate the leader's velocity. Moreover, the adaptive backstepping technique is used to compensate the effects of a dynamic model with the unknown time-invariant and time-varying parameters. From the Lyapunov stability theory, it is proved that the errors of the closed-loop system are uniformly ultimately bounded. Simulation results illustrate the effectiveness of the proposed control method.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.827-840
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• 2009

Let {$X_{ni}$ | $1{\leq}i{\leq}n,\;n{\geq}1$} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of ${\sum}^n_{t=1}a_{ni}X_{ni}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.855-867
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• 2005

Shattering or disintegration of mass is a well known phenomenon in fragmentation processes first introduced by Kol­mogorov and Filippop and extensively studied by many physicists. Though the mass is conserved in each break-up, the total mass decreases in finite time. We investigate this phenomenon in the n particle system. In this system, shattering can be interpreted such that, in uniformly bounded time on n, order n of mass is located in order o(n) of clusters. It turns out that the tagged particle processes associated with the systems are useful tools to analyze the phenomenon. For the newly defined stochastic shattering based on the above ideas, we derive far sharper conditions of fragmentation kernels which guarantee the occurrence of such a phenomenon than our previous work [9].

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• Proceedings of the KIEE Conference
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• 2006.10c
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• pp.327-329
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• 2006

A controller is proposed for the robust adaptive backstepping control of a class of uncertain nonlinear systems using nonlinear disturbance observer (NDO). The NDO is applied to estimate the time-varying lumped disturbance in each step, but a disturbance observer error does not converge to zero since the derivative of lumped disturbance is not zero. Then the fuzzy neural network (FNN) is presented to estimate the disturbance observer error such that the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The proposed control scheme guarantees that all the signals in the closed-loop are semiglobally uniformly ultimately bounded on the basis of the Lyapunov theorem. Simulation results are presented to illustrate the effectiveness and the applicability of the approaches proposed.