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.
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 te...
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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.
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.
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 pie...
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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.
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.
We are concerned here with a three-dimensional nonlinear mixed Volterra-Fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value pr...
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We are concerned here with a three-dimensional nonlinear mixed Volterra-Fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value problems. The existence of a unique solution will be proved. A new numerical method for solving these type of equations will be presented. The method is based upon three-dimensional block-pulse functions approximation. In addition convergence analysis of the method is discussed. Illustrative examples are included to demonstrate the validity and applicability of the technique. (C) 2014 Elsevier Inc. All rights reserved.
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