• Bulletin of the Korean Mathematical Society
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• 제57권1호
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• pp.251-274
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• 2020

We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the Farey map on the unit interval which generates an additive continued fraction algorithm. We explore some number theoretical properties of the Romik system. In particular, we prove an analogue of Lagrange's theorem in the case of the Romik system on the unit quarter circle, which states that a point possesses an eventually periodic digit expansion if and only if the point is defined over a real quadratic extension field of rationals.

• Proceedings of the IEEK Conference
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.1021-1024
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• 2000

In this paper, a neuro-fuzzy system for quantitative characterization of chaotic signals is proposed. The proposed system is differ from the previous methods in that the nonlinear functions of the nonlinear dynamical systems are calculated as the invariant factor. In the proposed neuro-fuzzy system, the nonlinear functions are determined by supervised learning. From the reconstructed nonlinear functions, the proposed system can generate extrapolated chaotic signals. This feature will help the study of nonlinear dynamical systems which require large number of chaotic data. To confirm the validity of the proposed system, nonlinear functions are reconstructed from 1-dimensional and 2-dimensional chaotic signals.

• Journal of the Korean Society of Marine Environment & Safety
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• 제24권3호
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• pp.325-331
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• 2018

This paper deals with the dynamical analysis of a vessel that leads to capsize in regular beam seas. The complete investigation of nonlinear behaviors includes sub-harmonic motion, bifurcation, and chaos under variations of control parameters. The vessel rolling motions can exhibit various undesirable nonlinear phenomena. We have employed a linear-plus-cubic type damping term (LPCD) in a nonlinear rolling equation. Using the fourth order Runge-Kutta algorithm with the phase portraits, various dynamical behaviors (limit cycles, bifurcations, and chaos) are presented in beam seas. On increasing the value of control parameter ${\Omega}$, chaotic behavior interspersed with intermittent periodic windows are clearly observed in the numerical simulations. The chaotic region is widely spread according to system parameter ${\Omega}$ in the range of 0.1 to 0.9. When the value of the control parameter is increased beyond the chaotic region, periodic solutions are dominant in the range of frequency ratio ${\Omega}=1.01{\sim}1.6$. In addition, one more important feature is that different types of stable harmonic motions such as periodicity of 2T, 3T, 4T and 5T exist in the range of ${\Omega}=0.34{\sim}0.83$.

• Smart Structures and Systems
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• 제5권1호
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• pp.69-79
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• 2009

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

• East Asian mathematical journal
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• 제31권5호
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• pp.743-751
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• 2015

In this paper, we consider a discrete ratio-dependent predator-prey system with harvesting effect. In order to investigate dynamical behaviors of this system, first we find out all fixed points of the system and then classify their stabilities by using their Jacobian matrices and local stability method. Next, we display some numerical examples to substantiate theoretical results and finally, we show numerically, by means of a bifurcation diagram, that various dynamical behaviors including cycles, periodic doubling bifurcation and chaotic bands can be existed.

• Proceedings of the KIEE Conference
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• 대한전기학회 1995년도 하계학술대회 논문집 B
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• pp.801-803
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• 1995

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptation controllers which guarrantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• Smart Structures and Systems
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• 제33권4호
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• pp.281-290
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• 2024

This work investigates the mechanical energy harvesting from smart and adaptive devices using magnetic interactions. The energy harvester is built from an elastic beam connected to an electric circuit by a magnetostrictive material that promotes energy transduction. Besides, magnetic interactions define the system stability characterizing multistable configurations. The adaptiveness is provided by magnets that can change their position with respect to the beam, changing the system configuration. A mathematical model is proposed considering a novel model to describe magnetic interactions based on the single-point magnet dipole method, but employing multiple points to represent the magnetic dipole, which is more effective to match experimental data. The adaptive behavior allows one to alter the system stability and therefore, its dynamical response. A nonlinear dynamics analysis is performed showing the possibilities to enhance energy harvesting capacity from the magnet position change. The strategy is to perform a system dynamical characterization and afterward, alter the energetic barrier according to the environmental energy sources. Results show interesting conditions where energy harvesting capacity is dramatically increased by changing the system characteristics.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2266-2270
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• 2005

In this paper, an internet based control application for dynamical systems is implemented. This implementation is maily targeted for the part of advanced control education. Intelligent control algorithms are implemented in a PC so that a client can remotely access the PC to control a dynamical system through the internet. Neural network is used as an on-line intelligent controller. To have on-line learning and control capability, the reference compensation technique is implemented as intelligent control hardware of combining a DSP board and an FPGA chip. GUIs for a user are also developed for the user's convenience. Actual experiments of motion control of a DC motor have been conducted to show the performance of the intelligent control though the internet and the feasibility of advanced control education.

• Journal of the Korean Institute of Telematics and Electronics
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• 제27권5호
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• pp.793-801
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• 1990

A single mode fiber-optic Mach-Zehnder interferometer for the measurement of strain is described. A fiber-optic strain gauge with great resolution and wide measurement range is realized. In order to varify the dynamic response, the measurements of strain below 1涅 with frequency range 5-50Hz are compared with a semiconductor strain gauge. We report theoretical evaluation for mechanical analysis, PZT-plate, the phase change in a fiber-optic strain gauge and a semiconductor strain gauge. The dynamical characteristics of a fiber-optic strain gauge and a semiconductor strain gauge output siganl show equivalent behavior. This result is shown in very good usage as the dynamical measurement of the low strain below 1涅 by this system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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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.