A simple direct method for solving three-dimensional linear Volterra integral equation of the second kind was introduced in this paper. Our method was demonstrated by applying three-dimensional block-pulse functions (...
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A simple direct method for solving three-dimensional linear Volterra integral equation of the second kind was introduced in this paper. Our method was demonstrated by applying three-dimensional block-pulse functions (3D-BPFs) and their operational matrix of integration. Indeed, we converted an integral equation to a linear system that can be easily solved. The convergence analysis of the method was discussed by convergence of 3D-BPFs and we found a bound for the error. Finally, some numerical examples illustrated that our method is feasible and efficient.
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.
In this paper, first, a numerical method is presented for solving generalized linear and nonlinear second-order two point initial and boundary value problems. The operational matrix of derivative is obtained by introd...
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In this paper, first, a numerical method is presented for solving generalized linear and nonlinear second-order two point initial and boundary value problems. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and block-pulse functions. The obtained operational matrix is used to reduce the linear or nonlinear equations with their initial or boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Finally, the efficiency of the proposed method is indicated by some numerical examples.
We construct two-dimensional hybrid functions from Lagrange polynomials and block-pulse functions. Using special properties of the functions for evaluating integral and derivatives, we develop an efficient algorithm f...
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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 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.
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 ...
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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.
This paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse...
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This paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side. The excellent properties of the hybrid functions together with the operational matrices of integration, product, and delay are presented. Using these matrices, the solution of the optimal control of delay systems is reduced to the solution of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The effectiveness of the method and the accuracy of the solution are shown in comparison with some other methods by illustrative examples
In this paper, an effective numerical approach based on a new two-dimensional hybrid of parabolic and block-pulse functions (2D-PBPFs) is presented for solving nonlinear partial quadratic integro-differential equation...
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In this paper, an effective numerical approach based on a new two-dimensional hybrid of parabolic and block-pulse functions (2D-PBPFs) is presented for solving nonlinear partial quadratic integro-differential equations of fractional order. Our approach is based on 2D-PBPFs operational matrix method together with the fractional integral operator, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations, which greatly simplifies the problem. By using Newton's iterative method, this system is solved, and the solution of fractional nonlinear partial quadratic integro-differential equations is achieved. Convergence analysis and an error estimate associated with the proposed method is obtained, and it is proved that the numerical convergence order of the suggested numerical method is O(h(3)). The validity and applicability of the method are demonstrated by solving three numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the exact solutions much easier.
In this study, an effective numerical approach based on the hybrid of block-pulse and parabolic functions (PBPFs) is suggested to obtain an approximate solution of a system of nonlinear stochastic It (o) over cap -Vol...
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In this study, an effective numerical approach based on the hybrid of block-pulse and parabolic functions (PBPFs) is suggested to obtain an approximate solution of a system of nonlinear stochastic It (o) over cap -Volterra integral equations of fractional order. For this aim, we first introduce these functions and express some of their properties and then calculate fractional and stochastic operational matrices of integration based on these functions. Using the properties of PBPFs and obtained operational matrices, the system of nonlinear stochastic It (o) over cap -Volterra integral equations of fractional order converts to a nonlinear system of algebraic equations which can be easily solved by using Newton's method. Moreover, in order to show the rate of convergence of the suggested approach, we present several theorems on convergence analysis and error estimation which demonstrate the rate of convergence of the proposed method for solving this nonlinear system is O(h(3)). Finally, two examples are included to illustrate the validity, applicability and efficiency of the proposed technique. (C) 2018 Elsevier B.V. All rights reserved.
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.
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