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 op...
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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.
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 co...
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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.
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 r...
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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.
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 ortho...
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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.
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 ...
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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.
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 secon...
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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.
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 ...
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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.
The operational matrix for performing integration of block-pulse functions is extended to inverse multidimensional Laplace transforms. The inversion algorithm only consists of two simple algebraic operations: multidim...
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The operational matrix for performing integration of block-pulse functions is extended to inverse multidimensional Laplace transforms. The inversion algorithm only consists of two simple algebraic operations: multidimensional bilinear transformation and long division of multivariable polynomials. The method is very suitable for computer programming.
This paper endeavors to formulate block-pulse functions to propose solutions for the Fredholm integral equations system. To begin with we describe the characteristic of block-pulse functions and will go on to indicate...
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This paper endeavors to formulate block-pulse functions to propose solutions for the Fredholm integral equations system. To begin with we describe the characteristic of block-pulse functions and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Numerical examples presented to illustrate the accuracy of the method. (c) 2004 Elsevier Inc. All rights reserved.
This article proposes a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation...
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This article proposes a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Some examples are presented to illustrate efficiency and accuracy of the proposed method. (C) 2007 Elsevier B.V. All rights reserved.
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