• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.277-287
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• 2007

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ of all bounded energy finite p-harmonic functions on G is in one to one corresponding to $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G')$ is also in an one to one correspondence with $\mathbf{R}^l$.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.11
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• pp.2139-2146
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• 2011

In this paper, a robust adaptive controller is proposed for trajectory tracking of robot manipulators with the unknown friction coefficient and bounded disturbance. A new adaptive control law is developed based on sliding mode and derived from the Lyapunov stability analysis. The introduction of a boundary layer solves the problem of chattering. The proposed adaptive controller is globally asymptotically stable and guarantees zero steady state error for joint positions. The estimated friction coefficients can also approach the actual coefficients asymptotically. A simulation example is provided to demonstrate the performance of the proposed algorithm.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.731-743
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• 2002

Let M be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on M. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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• pp.130-135
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• 2007

In this paper, a direct model reference adaptive fuzzy control (MRAFC) scheme is developed for the plant model whose structure is represented by the MIMO Takagi-Sugeno fuzzy model. The MRAFC scheme is proposed to provide asymptotic tracking of a reference signal lot the systems with uncertain or slowly time-varying parameters. The developed control law and adaptive law guarantee that all signals in the closed-loop system are bounded. In addition, the plant state tracks the state of the reference model asymptotically with time tot any bounded reference input signal.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.11
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• pp.503-509
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• 2002

In this paper, the robust non-fragile guaranteed cost control problem is studied for a class of linear large-scale systems with uncertainties and a given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties and controller gain variations. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1414-1417
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• 2003

In this paper, sliding mode controller for discrete-time nonlinear systems with uncertainties and disturbances are proposed. The concept of time-delay control (TDC) which consists of estimating the uncertain dynamics of the system through past observations of the system response is used. The proposed controller guarantees that the closed-loop system states are globally uniformly ultimately bounded (GUUB). It is also shown that the closed-loop system states are globally uniformly asymptotically stable (GUAS) if uncertainties are constant.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.7-11
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• 1991

The adaptive control of flexible joint manipulator is the focus of this paper. The full order flexible joint manipulator dynamic system does not allow the determination of a feedback linearization control as for rigid manipulators. This drawback is overcome by a model order reduction based on a singular perturbation strategy. The full order flexible joint manipulator dynamic model is adopted for derivation of the adaptive control law to damp out the elastic oscillations at the joints. It is shown that the joint position error will converge to zero asymptotically and that other signals remain bounded without precise knowledge of parameters of the manipulator and its joint flexibility.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10a
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• pp.451-456
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• 1990

We treat the problem of the robust tracking of a class of nonlinear systems which can be asymptotically decoupled in approximate sense by state variable feedback. A nonlinear control law is derived such that the tracking error in the closed loop system is uniformly bounded and tends to a certain small neighborhood of the origin. Simulation results show that simultaneous lateral and longitudinal maneuvers in airplane can be accurately performed in spite of uncertainty in stability derivatives.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.235-241
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• 1996

The ordinary least squares estimator of the disturbance variance in the linear regression model with stationary errors is shown to be asymptotically unbiased when the error process has a spectral density bounded from the above and away from zero. Such error processes cover a broad class of stationary processes, including ARMA processes.