• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.2393-2398
• /
• 2003

In this paper, we proposes a new fuzzy inference system for modeling nonlinear systems given input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the kernel-based method. The kernel-based method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated result illustrates the effectiveness of the proposed technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.1
• /
• pp.41-53
• /
• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

• 제어로봇시스템학회:학술대회논문집
• /
• 1988.10b
• /
• pp.772-776
• /
• 1988

In quantized control systems, the control values can take only given discrete (e.g. integer) values. In case of dealing with the control problem on the discrete-time, final-stage fixed, quantized control systems with multidimensional performance functions, the first thing, new definition on noninferior solutions in these systems is necessary because of their discreteness in state variables, and the efficient search for those solutions at final-stage is unavoidable for seeking their discrete-time optimal controls to these systems. In this paper, to the quantized control problem given by the formulation of Halkin-typed linear control systems with two performance functions, a new definition on noninferior solutions of this system control problem and a heuristic effective search on these noninferior solutions are stated. By use of these concepts, two definitions on noninferior solutions and the algorithm consisted of 8 steps and attained by geometric approaches are given. And a numerical example using the present algorithm is shown.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.2
• /
• pp.170-183
• /
• 2007

This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed $H_{\infty}$ performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust $H_{\infty}$ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.

• Journal of Korean Institute of Industrial Engineers
• /
• v.32 no.2
• /
• pp.74-81
• /
• 2006

In this paper, we deal with the separation of data by concurrently determined, piecewise nonlinear discriminant functions. Toward the end, we develop a new $l_1$-distance norm error metric and cast the problem as a mixed 0-1 integer and linear programming (MILP) model. Given a finite number of discriminant functions as an input, the proposed model considers the synergy as well as the individual role of the functions involved and implements a simplest nonlinear decision surface that best separates the data on hand. Hence, exploiting powerful MILP solvers, the model efficiently analyzes any given data set for its piecewise nonlinear separability. The classification of four sets of artificial data demonstrates the aforementioned strength of the proposed model. Classification results on five machine learning benchmark databases prove that the data separation via the proposed MILP model is an effective supervised learning methodology that compares quite favorably to well-established learning methodologies.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.145-159
• /
• 2011

The numerical solution to the linear and nonlinear and linear system of Fredholm and Volterra integral equations of the second kind are investigated. We have used crooked lines which includ the nodes specified by modified rationalized Haar functions. This method differs from using nominal Haar or Walsh wavelets. The accuracy of the solution is improved and the simplicity of the method of using nominal Haar functions is preserved. In this paper, the crooked lines with unknown coefficients under the specified conditions change the system of integral equations to a system of equations. By solving this system the unknowns are obtained and the crooked lines are determined. Finally, error analysis of the procedure are considered and this procedure is applied to the numerical examples, which illustrate the accuracy and simplicity of this method in comparison with the methods proposed by these authors.

• Journal of Korea Multimedia Society
• /
• v.17 no.11
• /
• pp.1279-1285
• /
• 2014

In this paper, we propose on image encryption method which uses NC(Non-linear Cycle) and 2D CAT(Two-Dimensional Cellular Automata Transform) in sequence to encrypt medical images. In terms of the methodology, we use NC to generate a pseudo noise sequence equal to the size of the original image. We then conduct an XOR operation of the generated sequence with the original image to conduct level 1 NC encryption. Then we set the proper Gateway Values to generate the 2D CAT basis functions. We multiply the generated basis functions by the altered NC encryption image to conduct the 2nd level 2D CAT encryption. Finally, we verify that the proposed method is efficient and extremely safe by conducting an analysis of the key spatial and sensitivity analysis of pixels.

• Journal of KSNVE
• /
• v.4 no.2
• /
• pp.137-146
• /
• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Structural Engineering and Mechanics
• /
• v.77 no.4
• /
• pp.535-547
• /
• 2021

This paper concerns with free torsional vibration analysis of size dependent circular nanobars with von kármán type nonlinearity. Although review of the literature suggests several studies employing nonlocal elasticity theory to investigate linear torsional behavior, linear/nonlinear transverse vibration and buckling of the nanoscale structures, so far, no study on the nonlinear torsional behavior of the nanobars, considering the size effect, has been reported. This study employs nonlocal elasticity theory along with a variational approach to derive nonlinear equation of motion of the nanobar. Then, the nonlinear equation is solved using the elliptic functions to extract the natural frequencies of the structure under fixed-fixed and fixed-free end conditions. Finally, the natural frequencies of the nanobar under different nanobar lengths, diameters, nonlocal parameters, and amplitudes of vibration are reported to illustrate the effect of these parameters on the vibration characteristics of the nanobars. In addition, the phase plane diagrams of the nanobar for various cases are reported.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.1
• /
• pp.47-56
• /
• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.