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A collocation method via block-pulse functions for solving delay fractional optimal control problems

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2017年第4期34卷 1215-1237页

作者： Hosseinpour, Soleiman Nazemi, Alireza Shahrood Univ Technol Sch Math Sci Dept Math POB ***-316 Shahrood Iran

A collocation scheme is applied to give an approximate solution of the fractional optimal control problems with delays in state and control. The operational matrix of fractional Riemann-Liouville integration, delay operational matrix and direct collocation method are used. The proposed technique is applied to transform the state and control variables into non-linear programming parameters at collocation points. The method is simple and computationally advantageous. Some examples are given to demonstrate the simplicity, clarity and powerfulness of the method.

关键词： delay fractional optimal control problems Caputo derivative block-pulse functions operational matrix delay operational matrix non-linear programming

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Numerical research of nonlinear system of fractional Volterra-Fredholm integral-differential equations via block-pulse functions and error analysis

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 345卷 159-167页

作者： Xie, Jiaquan Yi, Mingxu Taiyuan Univ Sci & Technol Coll Mech Engn Taiyuan 030024 Shanxi Peoples R China Beihang Univ Sch Aeronaut Sci & Technol Beijing 100191 Peoples R China

In this study, a numerical scheme for approximating the solutions of nonlinear system of fractional-order Volterra-Fredholm integral-differential equations (VFIDEs) has been proposed. This method is based on the orthogonal functions defined over [0, 1) combined with their operational matrices of integration and fractional-order differentiation. The main characteristic behind this approach is that it reduces such problems to a linear system of algebraic equations. In addition the error analysis of the system is investigated in detail. Lastly, several numerical examples are presented to test the effectiveness and feasibility of the given method. (C) 2018 Elsevier B.V. All rights reserved.

关键词： block-pulse functions Volterra-Fredholm integral-differential equations Numerical solutions Operational matrices Error analysis

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Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse functions

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APPLIED MATHEMATICS AND COMPUTATION 2004年第3期149卷 799-806页

作者： Maleknejad, K Mahmoudi, Y Iran Univ Sci & Technol Sch Math Tehran Iran Islamic Azad Univ Tehran Tehran Iran

In this paper, we use a combination of Taylor and block-pulse functions on the interval [0,1], that is called Hybrid functions, to estimate the solution of a linear Fredholm integral equation of the second kind. We convert the integral equation to a system of linear equations, and by using numerical examples we show our estimation have a good degree of accuracy. (C) 2003 Published by Elsevier Science Inc.

关键词： block-pulse functions Fredhohn integral equation operational matrix product operation Taylor polynomials

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ROBUST IDENTIFICATION OF SYSTEMS USING block-pulse functions

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1992年第3期139卷 308-316页

作者： DAI, H SINHA, NK Department of Electrical and Computer Engineering McMaster University Hamilton Canada

A robust method is employed to identify the unknown parameters of both linear and bilinear systems. Using block-pulse functions, this method expands the system input and output utilising an approach that minimises a robust criterion to reduce the effect of noise, especially large errors (called outliers) on the expansion coefficients. These coefficients are then used to obtain robust estimates of parameters. A Theorem showing convergence of this method is included. Simulation results provided in this paper demonstrate robustness and convergence of the proposed robust method. It can be concluded that this method is superior to the nonrobust version in the presence of noise, especially outliers.

关键词： block-pulse functions LINEAR SYSTEMS BILINEAR SYSTEMS

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Solution of Volterra's population model via block-pulse functions and Lagrange-interpolating polynomials

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2009年第2期32卷 127-134页

作者： Marzban, H. R. Hoseini, S. M. Razzaghi, M. Mississippi State Univ Dept Math & Stat Mississippi State MS 39762 USA Amirkabir Univ Dept Appl Math Tehran Iran Isfahan Univ Technol Dept Math Esfahan Iran

A numerical method for solving Volterra's Population model for population growth of a species in a closed system is proposed. Volterra's model is a nonlinear integro-differential equation where the integral tern) represents the effects of toxin. The approach is based on hybrid function approximations. The properties of hybrid functions that consist of block-pulse and Lagrange-interpolating polynomials are presented. The associated operational matrices of integration and product are then utilized to reduce the solution of Volterra's model to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. Applications are demonstrated through an illustrative example. Copyright (c) 2008 John Wiley & Sons, Ltd.

关键词： Volterra's population model hybrid function block-pulse functions Lagrange-interpolating polynomials nonlinear integro-differential equation orthogonal functions

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Numerical solutions of optimal control for time delay systems by hybrid of block-pulse functions and Legendre polynomials

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APPLIED MATHEMATICS AND COMPUTATION 2007年第2期184卷 849-856页

作者： Wang, Xing Tao Harbin Inst Technol Dept Math Harbin 150001 Peoples R China

Using the operational properties of general block-pulse functions and Legendre polynomials, the linear inverse time systems are transformed into a system of algebraic equations. The numerical solutions of the systems are derived. Moreover, applying the results to the linear quadratic optimal control problems, the approximate solutions of optimal control of time delay systems are derived. (c) 2006 Elsevier Inc. All rights reserved.

关键词： block-pulse functions Legendre polynomials time delay system optimal control

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Hybrid Fourier and block-pulse functions for applications in the calculus of variations

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2006年第8-9期83卷 695-702页

作者： Ghasemi, M. Babolian, E. Tavssoli Kajani, M. Teacher Training Univ Fac Math Sci & Comp Engn Tehran Iran Shahrekord Univ Dept Math Shahrekord Iran Islamic Azad Univ Dept Math Khorasgan Isfahan Iran

If we divide the interval [0, 1] into N sub-intervals, then hybrid Fourier and block-pulse functions on each sub-interval can approximate any function. This ability helps us to have more accurate approximations of piecewise continuous functions. Hence we obtain more accurate solutions to problems in the calculus of variations. In this article, we use a combination of Fourier and block-pulse functions on the interval [0, 1] to solve a variational problem in the solution of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.

关键词： series Fourier functions hybrid Fourier functions block-pulse functions operational matrix

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Applying the modified block-pulse functions to solve the three-dimensional Volterra-Fredholm integral equations

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APPLIED MATHEMATICS AND COMPUTATION 2015年 265卷 759-767页

作者： Mirzaee, Farshid Hadadiyan, Elham Malayer Univ Fac Math Sci & Stat Malayer Iran

The main aim of this work is to give further studies for the multi-dimensional integral equations. In this work, we solve special types of the three-dimensional Volterra-Fredholm linear integral equations of the second kind via the modified block-pulse functions. Some theorems are included to show convergence and advantage of the method. We solve some examples to investigate the applicability and simplicity of the method. The numerical results confirm that the method is efficient and simple. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Three-dimensional Volterra-Fredholm Modification block-pulse functions Error analysis

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Static output tracking control for non-linear polynomial time-delay systems via block-pulse functions

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2018年第3期41卷 194-205页

作者： Warrad, Bassem Iben Bouafoura, Mohamed Karim Braiek, Naceur Benhadj Univ Carthage Polytech High Sch Tunisia Lab Adv Syst Tunis Tunisia

In this paper, a new method is introduced to design static output tracking controllers for a class of nonlinear polynomial time-delay *** proposed technique is based on the projection of the controlled system and the associated linear reference model that it should follow over a basis of block-pulse functions. The useful properties of these orthogonal functions such as operational matrices jointly used with the Kronecker tensor product may transform the non-linear delay differential equations into linear algebraic equations depending only on parameters of the feedback *** least-squares method is then used for determination of the unknown parameters. Sufficient conditions for the practical stability of the closed-loop system are derived, and a domain of attraction is estimated. The implementation of the proposed method is illustrated on a double inverted pendulums benchmark as well as a two-degree-of- freedom mass-spring-damper system. The simulation results show the effectiveness of the developed technique.

关键词： Non-linear polynomial time-delay system static output tracking control practical stability block-pulse functions

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Design and experimental evaluation of block-pulse functions and Legendre polynomials observer for attitude-heading reference system

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ISA TRANSACTIONS 2021年 116卷 232-244页

作者： Keighobadi, Jafar Faraji, Javad Janabi-Sharifi, Farrokh Hamed, Mohammad Ali Univ Tabriz Fac Mech Engn Tabriz *** Iran Ryerson Univ Dept Mech & Ind Engn Toronto ON Canada

The main purpose of this paper is design and implementation of a new linear observer for an attitude and heading reference system (AHRS), which includes three-axis accelerometers, gyroscopes, and magnetometers in the presence of sensors and modeling uncertainties. Since the increase of errors over time is the main difficulty of low-cost micro electro mechanical systems (MEMS) sensors producing instable on-off bias, scale factor (SF), nonlinearity and random walk errors, development of a high-precision observer to improve the accuracy of MEMS-based navigation systems is considered. First, the duality between controller and estimator in a linear system is presented as the base of design method. Next, Legendre polynomials together with block-pulse functions are applied for the solution of a common linear time-varying control problem. Through the duality theory, the obtained control solution results in the block-pulse functions and Legendre polynomials observer (BPLPO). According to product properties of the hybrid functions in addition to the operational matrices of integration, the optimal control problem is simplified to some algebraic equations which particularly fit with low-cost implementations. The improved performance of the MEMS AHRS owing to implementation of BPLPO has been assessed through vehicle field tests in urban area compared with the extended Kalman filter (EKF). (C) 2021 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Orthogonal hybrid functions Legendre polynomials block-pulse functions Duality AHRS MEMS

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