• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.515-526
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• 2006

In this paper, we give a characterization of hyperbolic linear dynamical systems via the notions of various inverse shadowing. More precisely it is proved that for a linear dynamical system f(x)=Ax of ${\mathbb{C}^n}$, f has the ${\tau}_h$ inverse(${\tau}_h-orbital$ inverse or ${\tau}_h-weak$ inverse) shadowing property if and only if the matrix A is hyperbolic.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.73-76
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• 1996

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 the controller states in the absence and presence of saturating actuators as an objective function, the dynamical compensator which minimize the objective function are derived in an integrated fashion. The proposed dynamical compensator is a closed form of the plant and controller parameters. The proposed method guarantees total stability of resulting system. An illustrative example is given to show the effectiveness of the proposed method.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• Coupled systems mechanics
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• v.7 no.6
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.401-405
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• 1993

This paper presents a neuro adaptive control method for nonlinear dynamical systems based on artificial neural network systems. The proposed neuro adaptive controller consists of 3 layers artificial neural network system and parallel PD controller. At the early stage in learning or identification process of the system characteristics the PD controller works mainly in order to compensate for the inadequacy of the learning process and then gradually the neuro contrller begins to work instead of the PD controller after the learning process has proceeded. From the simulation studies the neuro adaptive controller is seen to be robust and works effectively for nonlinear dynamical systems from a practical applicational points of view.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1135-1138
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• 1990

In this paper, we study the pole assignment problem for three-dimensional systems. We transform the denominator of transfer functions of the closed-loop system into the product of three stable one-dimensional polynomials, by performing two-dimensional dynamical feedback and input transformation on the given three-dimensional systems. In the next, we consider the possibility that these two-dimensional dynamic compensators are realizable, thoroughly, and propose the counter-measure in case that they are not realizable. And, we obtain the conditions so that the closed-loop three-dimensional systems are stable. Moreover, we calculate the dynamical dimension which is necessary for the pole assigntmnt, and suggest the pole assignmnt method with the lowest dynamical dimnsion.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.529-539
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• 2016

In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.368-373
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• 2005

This paper presents a new framework for the traffic flow control based on integrated model descriptions as the Hybrid Dynamical System (HDS).

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.327-335
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• 2018

In this paper, we present the construction of natural invariant measures so called SRB(Sinai-Ruelle-Bowen) measures by the properties of geometric t-potential and Bowen's equation for the hyperbolic attractors.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1115-1125
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• 2023

This paper deals with the controllability of linear and nonlinear generalized fractional dynamical systems in finite dimensional spaces. The results are obtained by using fractional calculus, Mittag-Leffler function and Schauder's fixed point theorem. Observability of linear system is also discussed. Examples are given to illustrate the theory.