• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.449-463
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• 1998

In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^{r}$ dynamical systems (or $C^{r}$ diffeomor-phisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^{r}$ dynamical systems.stems.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.575-586
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• 2007

We introduce here notions of chain recurrent sets, attractors and its basins for general dynamical systems and prove important properties including (i) the chain recurrent set CR(f) of f on a metric space (X, d) is the complement of the union of sets B(A) -A as A varies over the collection of attractors and (ii) genericity of general dynamical systems.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.157-172
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• 1998

A numerical method is proposed for dynamical systems. We utilize the fact that special matrix exponentials can be exactly evaluated by the intrinsic library functions. Numerical examples are given, which show that the relative error s of the proposed method converge to a small constant and that the method faithfully approximates the dynamics of the nonlinear differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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• pp.341-355
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• 2017

This paper is devoted to some dynamical properties such as transitivity, mixing and specification of two discrete dynamical systems (X, f) and ($2^X$, ${\bar{f}}$) on compact metric spaces.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.397-406
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• 1997

In this paper we introduce GESS method and show that dynamics of the system ｙ＇=A(s,t,y) ｙ is more faithfully approxi-mated by GESS method that by Euler method. Numerical experiments are given for the comparison of GESS method with Euler method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1165-1168
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• 1996

The neural network approach has been shown to be a general scheme for nonlinear dynamical system identification. Unfortunately the error surface of a Multilayer Neural Network(MNN) that widely used is often highly complex. This is a disadvantage and potential traps may exist in the identification procedure. The objective of this paper is to identify a nonlinear dynamical systems based on Radial Basis Function Networks(RBFN). The learning with RBFN is fast and precise. This paper discusses RBFN as identification procedure is based on a nonlinear dynamical systems. and A design method of model follow control system based on RBFN controller is developed. As a result of applying this method to inverted pendulum, the simulation has shown that RBFN can be used as identification and control of nonlinear dynamical systems effectively.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.141-150
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• 1998

This paper presents a dynamical anti-reset windup (ARW) compensation method for saturating control systems with multiple controllers and/or multiloop configuration. By regarding the difference of controller states in the absence and presence of saturating actuators as an objective function, the dynamical compensator which minimizes the objective function is derived in an integrated fashion. The proposed dynamical compensator is a closed form of plant and controller parameters. The resulting dynamics of compensated controller reflects the linear closed-loop system. The proposed method guarantees total stability of the resulting system. The effectiveness of the proposed method is illustrated by applying it to a servo motor control system. The paper is an extension of the results in Park and Choi[1].

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.575-591
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• 2018

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.703-713
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• 2012

In this paper we study ${\omega}$-limit sets and attraction of non-autonomous discrete dynamical systems. We introduce some basic concepts such as ${\omega}$-limit set and attraction for non-autonomous discrete system. We study fundamental properties of ${\omega}$-limit sets and discuss the relationship between ${\omega}$-limit sets and attraction for non-autonomous discrete dynamical systems.

• International Journal of Safety
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• v.10 no.2
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• pp.10-15
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• 2011

The reconfigurable control systems based on feedback controls are utilized to compensate for damages of actuators in control systems. Such systems have multiple feedback controls and switch them in accordance with the degrees of the failures of the actuators. In order to be able to assess those systems, this paper develops a method to obtain reliabilities of reconfigurable dynamical systems which are interconnected in parallel / series configuration. By calculating reliabilities of interconnected dynamical systems, it is possible to assess many dynamical systems by comparing their reliabilities. Firstly, reliabilities of subsystems are obtained according to the definitions of the failures in terms of robust reliability for each subsystem. Then, the reliability of overall system is calculated from reliabilities of subsystems, using the methodology employed for probabilistic safety assessment. Failure rates of subsystems with feedbacks for reconfiguration change in certain time periods because of the switching of feedback controls. In order to deal with this, combinations of subsystems which compose overall system for each time period are derived by the methodology mentioned above and then integrated to calculate the reliability of overall system for a specific time. An illustrative example shows the validity and details of the proposed method.