• Journal of the Korean Society for Precision Engineering
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• v.31 no.3
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• pp.253-259
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• 2014

This study proposes a map-based control method to improve a vehicle's lateral stability, and the performance of the proposed method is compared with that of the conventional model-referenced control method. Model-referenced control uses the sliding mode method to determine the compensated yaw moment; in contrast, the proposed map-based control uses the compensated yaw moment map acquired by vehicle stability analysis. The vehicle stability region is calculated by a topological method based on the trajectory reversal method. The performances of model-referenced control and map-based control are compared under various road conditions and driving inputs. Model-referenced control uses a control input to satisfy the linear reference model, and it generates unnecessary tire lateral forces that may lead to worse performance than an uncontrolled vehicle with step steering input on a road with low friction coefficient. The simulation results show that map-based control provides better stability than model-referenced control.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1309-1318
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• 2020

In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.2
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• pp.108-114
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• 1996

We present proofs of the stability and convergence of Self-organizing feature map (SOFM) neural network with time-invarient learning rate and binary reinforcement function. One of the major problems in Self-organizing feature map neural network concerns with learning rate-"Kalman Filter" gain in stochsatic control field which is monotone decreasing function and converges to 0 for satisfying minimum variance property. In this paper, we show that the stability and convergence of Self-organizing feature map neural network with time-invariant learning rate. The analysis of the proposed algorithm shows that the stability and convergence is guranteed with exponentially stable and weak convergence properties as well.s as well.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.827-845
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• 2005

In this paper, we present a general method for the stability analysis of some bursting models. Our method is geometric in the sense that we consider a flow-defined return map defined on a section and determine when the map is a contraction. We find that there are three different stability types in the codimension-1 planar bursters.

• Journal of Theoretical and Applied Mechanics
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• v.1 no.1
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• pp.29-67
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• 1995

A procedure is formulated, in this paper, to compute the bifurcation modes born by the stability change of normal modes, and to compute the forced responses associated with bifurcation modes in inertially and elastically coupled nonlinear oscillators. It is assumed that a saddle-loop is formed in Poincare map at the stability chage of normal modes. In order to test the validity of procedure, it is applied to one-to-one internal resonant systems in which the solutions are guaranteed within the order of a small perturbation parameter. The procedure is also applied to the exact system in which normal modes are written in exact form and the stability of normal modes can be exactly determined. In this system the stability change of normal modes occurs several times so that various types of bifurcation modes are created. A method is described to identify a fixed point on Poincare map as one of bifurcation modes. The limitations and advantage of proposed procedure are discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.6_spc
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• pp.635-643
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• 2016

A stability theory of a damped cantilever column under sub-tangential follower forces is first summarized based on the stability map. It is then demonstrated that internal and external damping can be exactly transformed to Rayleigh damping so that the damping coefficients can be effectively determined using proportional damping. Particularly a parametric study with variation of damping coefficients is performed in association with flutter loads of Beck's column and it is shown that two damping coefficients can be correctly estimated for real systems under the assumption of Rayleigh damping. Finally a frequency equation of a cantilever beam subjected to both a sub-tangentially follower force and two kinds of damping forces is presented in the closed-form and its stability maps are constructed and compared with FE solutions in the practical range of damping coefficients.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.167-176
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• 2010

Let (B, $\check{g}$) and (N, $\hat{g}$) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold $B\;{\times}_f\;N\;:=\;(B\;{\times}\;N,\;\check{g}\;+\;f{\hat{g}}$) to be Einstein, and obtain a complete condition for the Einstein warped product manifold $B\;{\times}_f\;N$ to be weakly stable. Moreover, we get a complete condition for the map i : ($B,\;\check{g})\;{\times}\;(N,\;\hat{g})\;{\rightarrow}\;B\;{\times}_f\;N$, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for $B\;{\times}_f\;N$ to be Einstein.

• Economic and Environmental Geology
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• v.33 no.1
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• pp.51-59
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• 2000

As a part of natural hazard assessment, regional slope stability analysis was conducted using Geoscientific Information System (GIS) in the northern area of Chungju Lake. Selected factors which affect the slope stability in the study area were lithology, soil, density of lineament, groundwater level, dip of slope, aspect of slope, and geological engineering properties. Geological structural domains were determined by collected data of joint orientation from about 200 sites in order to produce a slope instability map. Potential type of failure and its direction could be expected through the domains. And a slope instability map was produced, comparing the representative orientations of the domains with the orientations of the slopes which were made through TIN module in ARC/INFO. Under the consideration of environmental geological characteristics of the study area, rating and weighting of each factor of slope stability analysis were decided and spatial analysis of regional slope stability was couducted through overlaying technique of GIS. The result of areal distribution of slope stability showed that the most unstable area was the area between Mt. Pudae and Mt. Jubong, and the northern area of the railway station, Samtan.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.31-34
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• 2003

In this paper, we introduce the notion of F-harmonic maps and we study the stability of F-harmonic map.

• 한국연소학회:학술대회논문집
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• 2012.04a
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• pp.77-78
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• 2012

To predict combustion instability in actual full-scale combustion chamber of rocket engines, air-injection test is proposed with scaling techniques. From the data, damping factors have been obtained as a function of hydraulic parameter and the data give us instability map. Two instability regions are presented and it is found that they coincide reasonably with them from hot-fire test with full-scale flow rates. Accordingly, the proposed approach can be applied cost-effectively to stability rating of jet injectors when mixing of fuel and oxidizer jets is the dominant process in instability triggering.