• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.249-257
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• 1995

In this paper, we demeonstrate that neural networks can be used effectively for the control of nonlinear dynamical system. To adaptively control a plant, there are two distinct approach. these are direct control and indirect control. Both direct and Indirect adaptive control are trained using static back propagation. In indirect, using the resulting identification model, which contains neural networks and linear dynamical elements as subsystems, the parameters of the controller are adjusted.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1421-1431
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• 2021

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C⁰-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1101-1123
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• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.469-469
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• 2000

The use of orthogonal functions with the aim of adapting the system and signal representation to the specific properties of the systems and signals has a long history. A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized orthogonal functions. It is shown that there exist orthogonal functions that are generated by stable linear dynamical systems.

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.325-332
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• 1988

• Coupled systems mechanics
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• v.4 no.3
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• pp.251-262
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• 2015

The current paper aims at investigating the nonlinear dynamical behaviour of an electrically actuated microcantilever. The microcantilever is excited by a combination of AC and DC voltages. The nonlinear equation of motion of the microcantilever is obtained by means of force and moment balances. A high-dimensional Galerkin scheme is then applied to reduce the equation of motion to a discrete model. A numerical technique, based on the pseudo-arclength continuation method, is used to solve the discretized model. The electrostatic deflection of the microcantilever and static pull-in instabilities, due to the DC voltage, are analyzed by plotting the so-called DC voltage-deflection curves. At the simultaneous presence of the DC and AC voltages, the nonlinear dynamical behaviour of the microcantilever is analyzed by plotting frequency-response and force-response curves.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.93-102
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• 2005

In this paper, we introduce the history of dynamical systems and the notion of the H-shadowing property. And we study some relationships between the H-shadowing property and other dynamical properties such as expansivity and topological stability.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.2
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• pp.189-199
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• 1999

This paper presents an optimization algorithm for a stable Self Dynamic Neural Network(SDNN) using genetic algorithm. Optimized SDNN is applied to a problem of controlling nonlinear dynamical systems. SDNN is dynamic mapping and is better suited for dynamical systems than static forward neural network. The real-time implementation is very important, and thus the neuro controller also needs to be designed such that it converges with a relatively small number of training cycles. SDW has considerably fewer weights than DNN. Since there is no interlink among the hidden layer. The object of proposed algorithm is that the number of self dynamic neuron node and the gradient of activation functions are simultaneously optimized by genetic algorithms. To guarantee convergence, an analytic method based on the Lyapunov function is used to find a stable learning for the SDNN. The ability and effectiveness of identifying and controlling a nonlinear dynamic system using the proposed optimized SDNN considering stability is demonstrated by case studies.

• International Journal of Control, Automation, and Systems
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• v.6 no.3
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• pp.401-412
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• 2008

This paper discusses a design methodology of cooperative path planning for dynamical multi-agent systems with spatial and temporal constraints. The cooperative behavior of the multi-agent systems is specified in terms of the objective function in an optimization formulation. The path of achieving cooperative tasks is then generated by the optimization formulation constructed based on a differential flatness approach. Three scenarios of multi-agent tasking are proposed at the cooperative task planning framework. Given agent dynamics, both spatial and temporal constraints are considered in the path planning. The path planning algorithm first finds trajectory curves in a lower-dimensional space and then parameterizes the curves by a set of B-spline representations. The coefficients of the B-spline curves are further solved by a sequential quadratic programming solver to achieve the optimization objective and satisfy these constraints. Finally, several illustrative examples of cooperative path/task planning are presented.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.12
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• pp.1155-1163
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• 2004

Extracellular signal-regulated kinase (ERK) signaling pathway is one of the mitogen-activated protein kinase (MAPK) signal transduction pathways. This pathway is known as pivotal in many signaling networks that govern proliferation, differentiation and cell survival. The ERK signaling pathway comprises positive and negative feedback loops, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. In this paper, we attempt to model the ERK pathway by considering both of the positive and negative feedback mechanisms based on Michaelis-Menten kinetics. In addition, we propose a fraction ratio model based on the mass action law. We first develop a mathematical model of the ERK pathway with fraction ratios. Secondly, we analyze the dynamical properties of the fraction ratio model based on simulation studies. Furthermore, we propose a concept of an inhibitor, catalyst, and substrate (ICS) controller which regulates the inhibitor, catalyst, and substrate concentrations of the ERK signal transduction pathway. The ICS controller can be designed through dynamical analysis of the ERK signaling transduction pathway within limited concentration ranges.