• Journal of Mechanical Science and Technology
• /
• v.19 no.11
• /
• pp.1975-1987
• /
• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.

• International Journal of Control, Automation, and Systems
• /
• v.4 no.3
• /
• pp.293-301
• /
• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• Geomechanics and Engineering
• /
• v.17 no.3
• /
• pp.227-236
• /
• 2019

In practice, the natural slopes are frequently with soils of spatial properties and irregular features. The traditional limit analysis method meets an inherent difficulty to deal with the stability problem for such slopes due to the normal condition in the associated flow rule. To overcome the problem, a novel technique based on the upper bound limit analysis, which is called the discretization technique, is employed for the stability evaluation of complex slopes. In this paper, the discretization mechanism for complex slopes was presented, and the safety factors of several examples were calculated. The good agreement between the discretization-based and previous results shows the accuracy of the proposed mechanism, proving that it can be an alternative and reliable approach for complex slope stability analysis.

• Journal of Mechanical Science and Technology
• /
• v.20 no.7
• /
• pp.950-960
• /
• 2006

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.

• East Asian mathematical journal
• /
• v.30 no.5
• /
• pp.609-616
• /
• 2014

In this paper we consider hyperbolic equations related to the p-Laplacian with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• East Asian mathematical journal
• /
• v.26 no.3
• /
• pp.403-413
• /
• 2010

In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.5 no.2
• /
• pp.374-388
• /
• 2011

Biometric discretization is a process of transforming continuous biometric features of an identity into a binary bit string. This paper mainly focuses on improving the global discretization method - a discretization method that does not base on information specific to each user in bitstring extraction, which appears to be important in applications that prioritize strong security provision and strong privacy protection. In particular, we demonstrate how the actual performance of a global discretization could further be improved by embedding a global discriminative feature selection method and a Linearly Separable Subcode-based encoding technique. In addition, we examine a number of discriminative feature selection measures that can reliably be used for such discretization. Lastly, encouraging empirical results vindicate the feasibility of our approach.

• ETRI Journal
• /
• v.45 no.4
• /
• pp.704-712
• /
• 2023

This paper presents a flexible finite-difference technique for analyzing the nonuniform guiding structures. Because the voltage and current variations along the nonuniform structure differ for each segment, this work considers the adaptable discretization steps. This technique increases the accuracy of the final response. Moreover, by applying the singular value decomposition and discarding the nonprincipal singular values, an optimal lower rank approximation of the discretization matrix is obtained. The computational cost of the introduced method is significantly reduced using the optimal discretization matrix. Also, the proposed method can be extended to the nonuniform waveguides. The technique is verified by analyzing several practical transmission lines and waveguides with nonuniform profiles.

• Database Research
• /
• v.34 no.3
• /
• pp.159-169
• /
• 2018

Discretization of continuous variables intended to improve the performance of various algorithms such as data mining by transforming quantitative variables into qualitative variables. If we use appropriate discretization techniques for data, we can expect not only better performance of classification algorithms, but also accurate and concise interpretation of results and speed improvements. Various discretization techniques have been studied up to now, and however there is still demand of research on discretization studies. In this paper, we propose a new discretization technique to set the cut-point using Wasserstein distance with considering the distribution of continuous variable values with classes of data. We show the superiority of the proposed method through the performance comparison between the proposed method and the existing proven methods.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.2562-2567
• /
• 2005

This paper suggests a new method discretization of nonlinear system using Taylor series expansion and zero-order hold assumption. This method is applied into the sampled-data representation of a nonlinear system with input time delay. Additionally, the delayed input is time varying and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. Them mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. And 'hybrid' discretization scheme that result from a combination of the ‘scaling and squaring' technique with the Taylor method are also proposed, especially under condition of very low sampling rates. The computer simulation proves the proposed algorithm discretized the nonlinear system with the variable time-delayed input accurately.