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Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations in two-dimensional spaces based on block pulse functions

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2017年 317卷 565-572页

作者： Xie, Jiaquan Huang, Qingxue Zhao, Fuqiang Taiyuan Univ Sci & Technol Coll Mech Engn Taiyuan 030024 Shanxi Peoples R China Taiyuan Univ Technol Coll Mech Engn Taiyuan 030024 Shanxi Peoples R China Shanxi Prov Key Lab Met Device Design Theory & Te Taiyuan Peoples R China

In this paper, the numerical technique based on block pulse functions (BPFs) has been developed to approximate the solutions of nonlinear Volterra-Fredholm-Hammerstein integral equations in two-dimensional spaces. These functions are orthogonal and have compact support on [0, 1]. The proposed method reduces the integral equations to a system of nonlinear algebraic equations that can be easily solved by any numerical method. Also, the convergence of the proposed approach is discussed. Furthermore, in order to show the accuracy and reliability of the above-mentioned algorithm, the new approach is verified through some numerical examples. (C) 2016 Elsevier B.V. All rights reserved.

关键词： block pulse functions Operational matrix Nonlinear integral equation Volterra-Fredholm-Hammerstein

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Identification of fractional-order systems with time delays using block pulse functions

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2017年 91卷 382-394页

作者： Tang, Yinggan Li, Ning Liu, Minmin Lu, Yao Wang, Weiwei Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Liren Coll Qinhuangdao 066004 Hebei Peoples R China

In this paper, a novel method based on block pulse functions is proposed to identify continuous-time fractional-order systems with time delays. First, the operational matrices of block pulse functions for fractional integral operator and time delay operator are derived. Then, these operational matrices are applied to convert the continuous-time fractional-order systems with time delays to an algebraic equation. Finally, the system's parameters along with the differentiation orders and the time delays are all simultaneously estimated through minimizing a quadric error function. The proposed method reduces the computation complexity of the identification process, and also it does not require the system's differentiation orders to be commensurate. The effectiveness of the proposed method are demonstrated by several numerical examples. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Identification Fractional order systems Time delays block pulse functions Operational matrix

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Optimal control problem for a class of bilinear systems via block pulse functions

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2017年第3期34卷 973-986页

作者： Balatif, Omar Rachik, Mostafa Labriji, El Houssine Rachik, Zineb Hassan II Univ Mohammedia Lab Anal Modeling & Simulat Dept Math & Comp Sci Fac Sci Ben MSik BP 7955 Casablanca Morocco

This paper deals with an optimal control problem with quadratic cost for a class of bilinear systems using the orthogonal functions technique. The main idea of this technique is that it reduces the problem to solving a system of algebraic equations, thus simplifying the problem. The control variable and the state variables are approximated by block pulse functions series. Then the system dynamics is transformed into systems of algebraic equations. Finally, numerical results are given to illustrate the proposed method.

关键词： bilinear system optimal control orthogonal functions block pulse functions

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Identification of Structural Dynamic Parameters Using block pulse functions and Recursive Least-Squares Algorithm

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF CIVIL ENGINEERING 2017年第2期41卷 149-158页

作者： Ajorloo, Yaser Hosseini Ghaffarzadeh, Hosein Univ Tabriz Fac Civil Engn Tabriz Iran

System identification in recent years with the development of dynamic testing of structures has become one of the useful methods for structural health monitoring and damage detection and also finite element model updating. Identification of structural dynamic parameters is performed by using excitation-response data and includes physical parameters such as mass, stiffness and damping matrices and/or modal parameters such as natural frequencies, damping ratios and modal shapes. This paper presents a new method to identify the dynamical parameters of shear building based on continuous-time state-space estimation using block pulse functions and least-squares technique. block pulse functions are a set of orthogonal functions with piecewise constant values and useful tools in analysis, identification and system science. Assuming that the input-outputs data of the original system are known, their block pulse coefficients can be calculated by numerical methods, and using block pulse operational matrix, state-space equations of dynamical system are transformed into block pulse regression equations. Based on these equations, the plant matrix is estimated using least-squares algorithm. Then, the physical and modal parameters of structure are identified based on eigenmode data of the estimated plant matrix. To prove the validity and feasibility of the proposed method, numerical simulation of a shear building which is equipped with sensors on all floors and excited by four different normally distributed random signals and an earthquake is presented. The results reveal the proposed method can be beneficial in structural identification with less computational expenses and high accuracy.

关键词： System identification block pulse functions Continuous-time state space Least-squares algorithm Eigenmode data

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Numerical Solutions of Nonlinear Optimal Control Systems With block pulse functions 13

Numerical Solutions of Nonlinear Optimal Control Systems Wit...

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International Conference on Advanced Systems and Electric Technologies (IC_ASET)

作者： Aousgi, Ines Sansa Elloumi, Salwa Braiek, Naceur Benhadj Polytech Sch Tunisia Lab Syst Avances La Marsa Tunisia

ISBN: (纸本)9781538644492

In this work, we develop a nonlinear optimal control using the direct approach based on the block pulse functions (BPFs) parametrization technique. Using this numerical approach, we will transform the original nonlinear optimal control problem into a nonlinear programming which is easier to solve. This approach is implemented on a polynomial nonlinear state space description using the Kronecker product and the power of matrices properties. An illustrative example of nonlinear system is included to demonstrate the validity and the effectiveness of the proposed approach.

关键词： block pulse functions Direct Approach Kronecker product Nonlinear programming Optimal Feedback Control

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The application of block pulse functions for solving higher-order differential equations with multi-point boundary conditions

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ADVANCES IN DIFFERENCE EQUATIONS 2016年第1期2016卷 1页

作者： Avazzadeh, Zakieh Heydari, Mohammad Nanjing Normal Univ Sch Math Sci Inst Math Nanjing 210023 Jiangsu Peoples R China Yazd Univ Dept Math POB 89195-41 Yazd Iran

In this paper, the block pulse function method is proposed for solving high-order differential equations associated with multi-point boundary conditions. Although the orthogonal block pulse functions frequently have been applied to approximate the solution of ordinary differential equations associated with the initial conditions, the presented method provides the flexibility with respect to multi-point boundary conditions in separated or non-separated forms. This technique, which may be named the augmented block pulse function method, reduces a system of high-order boundary value problems of ordinary differential equations to a system of algebraic equations. The illustrated results confirm the computational efficiency, reliability, and simplicity of the presented method.

关键词： ordinary differential equations block pulse functions boundary value problem multi-point value problem separated or non-separated boundary conditions

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Parameter identification of fractional order systems using block pulse functions

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SIGNAL PROCESSING 2015年 107卷 272-281页

作者： Tang, Yinggan Liu, Haifang Wang, Weiwei Lian, Qiusheng Guan, Xinping Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066004 Hebei Peoples R China Minist Educ Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Hebei Peoples R China

In this paper, a novel method is proposed to identify the parameters of fractional-order systems. The proposed method converts the fractional differential equation to an algebraic one through a generalized operational matrix of block pulse functions. And thus, the output of the fractional system to be identified is represented by a matrix equation. The parameter identification of the fractional order system is converted to a multi-dimensional optimization problem, whose goal is to minimize the error between the output of the actual fractional order system and that of the identified system. The proposed method can simultaneously identify the parameters and the fractional differential orders of the fractional order system and avoid the drawbacks in the literature that the fractional differential orders should be known or commensurate. Furthermore, the proposed method avoids complex calculations of the fractional derivative of input and output signals. Illustrative examples covering both fractional and integer systems are given to demonstrate the validity of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Identification Fractional order system block pulse functions Operational matrix

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Numerical solution of Volterra integral-algebraic equations using block pulse functions

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APPLIED MATHEMATICS AND COMPUTATION 2015年 263卷 165-170页

作者： Balakumar, V. Murugesan, K. Natl Inst Technol Dept Math Tiruchirappalli 620015 Tamil Nadu India

This paper presents a method for computing numerical solutions for linear Volterra integral-algebraic equations using block pulse functions. The problem is transformed to a linear lower triangular system of algebraic equations using the operational matrix associated with block pulse functions. Convergence result and numerical examples are presented to illustrate the efficiency and applicability of the method. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Approximate solutions block pulse functions Numerical method Integral-algebraic equations

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A NUMERICAL SOLUTION OF THE ARBITRARY ORDER WEAKLY SINGULAR INTEGRAL USING block-pulse functions AND APPLICATIONS

ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS

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ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2016年第36期36卷 629-638页

作者： Song, Hao Huang, Jun Yi, Mingxu Pan, Yalin Beihang Univ Sch Aeronaut Sci & Technol Beijing 100191 Peoples R China

The purpose of this paper is to obtain the approximation of the arbitrary order weakly singular integral using block-pulse functions. The obtained results can be used to solve the numerical solution of higher order linear and nonlinear weakly singular Volterra integral equation of the second kind. Furthermore, the initial equations are transformed into a system of algebraic equations. Finally, some examples are given to demonstrate the validity and applicability of this approach, results of these examples show that this new method is an efficient algorithm.

关键词： weakly singular integral weakly singular integral equation block pulse functions operational matrix numerical solution

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RETRACTED: Solution of nonlinear Fredholm integro-differential equations using a hybrid of block pulse functions and normalized Bernstein polynomials (Retracted Article)

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2014年 260卷 258-265页

作者： Behiry, S. H. King Abdulaziz Univ Jeddah Community Coll Gen Required Courses Dept Jeddah 21589 Saudi Arabia

A numerical method for solving nonlinear Fredholm integro-differential equations is proposed. The method is based on hybrid function approximations. The properties of a hybrid of block pulse functions and orthonormal Bernstein polynomials are presented and utilized to reduce the problem to the solution of nonlinear algebraic equations. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Nonlinear Fredholm integro-differential equations Hybrid functions block pulse functions Bernstein polynomials

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