Solving a class of nonlinear optimal control problems via he’s variational iteration method

Shirazian, Mohammad; Effati, Sohrab

doi:10.1007/s12555-012-0205-z

Cited by 25 publications

(23 citation statements)

References 10 publications

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“…Moreover they compared with simulation curves that computed by fourth-order Runge-Kutta method. In comparison with [4], the curves are similar but the computations and consumed time is less.…”

Section: Min J U T Dt S To X X T X T U T T X Xmentioning

confidence: 88%

“…Therefore, many researchers have tried to find an approximate solution for these nonlinear TPBVP's. Regarding this fact, in the recent years, some new applications of finding an approximate analytical solution methods for TPBV differential systems have been presented to solve the related optimal control problems, such as Variational Iteration Method [4], Homotopy method [5], Optimal Homotopy Perturbation Method [6]. In sequential, here, we employ DTM to solve a class of nonlinear optimal control problems.…”

Section: The Journal Of Mathematics and Computer Sciencementioning

confidence: 99%

“…The first ones, has the terminal condition and in the other one, the terminal condition is free. The selected examples were solved in [4] by VIM. More than our new method, we solved the related TPBVP's by fourth-order Runge-Kutta method as well to have a suitable comparison.…”

Section: Numerical Examples and Comparisonmentioning

confidence: 99%

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Solving A Class Of Nonlinear Optimal Control Problems By Differential Transformation Method

Fakharzadeh¹,

Hashemi²

2012

J. Math. Computer Sci.

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Based on the Differential Transformation Method (DTM), a solution procedure for solving a class of nonlinear quadratic optimal control problems is presented in this paper. The reason for selecting this solution procedure is the less computational cost in comparison with the ordinary solution methods of original problem. First, the problem is converted to a two-point boundary value problem then the new problem is transferred into a set of algebraic equations by applying the differential transformation properties. By presenting the algorithmic solution procedure, two numerical examples are given to demonstrate the simplicity and efficiency of the new method.

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Section: Min J U T Dt S To X X T X T U T T X Xmentioning

confidence: 88%

Section: The Journal Of Mathematics and Computer Sciencementioning

confidence: 99%

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Solving A Class Of Nonlinear Optimal Control Problems By Differential Transformation Method

Fakharzadeh¹,

Hashemi²

2012

J. Math. Computer Sci.

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“…Figures 12 and 13 show the control function approximation and its corresponding error. This problem is solved in [27] by a variational method. For this example we have H (x(t), u(t), p(t), t) = u(t) 2 + p(0.5x 2 (t)sin(x(t)) + u(t)).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Approximating the Solution of Optimal Control Problems by Fuzzy Systems

Pakdaman

Effati

2015

Neural Process Lett

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In this paper, the ability of fuzzy systems is used to estimate the solution of crisp optimal control problems. To solve an optimal control problem, first the well-known EulerLagrange conditions are obtained and then, the solution of these conditions is approximated by defining a trial solution based on fuzzy systems. The parameters of fuzzy systems are adjusted by an optimization algorithm. Numerical examples and comparisons with exact solutions reveal the capability and accuracy of proposed method.

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“…Unlike the traditional numerical methods, VIM needs no discretization, linearization, transformation, or perturbation. The VIM has been applied in a wide range of problems successfully, such as partial differential equations [22], fractional differential equations [23], integrodifferential equations [31] and nonlinear problems [26,28]. The main aim in this study is to effectively employ VIM to establish exact solutions and numerical results of linear and non-linear time-varying multi-delay systems and study the convergence of the method.…”

Section: Introductionmentioning

confidence: 99%

Solution of linear time-varying multi-delay systems via variational iteration method

Mirhosseini-Alizamini¹,

Effati²,

Heydari³

2016

J. Math. Computer Sci.

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This work presents an approximate solution method for the linear time-varying multi-delay systems and time delay logistic equation using variational iteration method. The method is based on the use of Lagrange multiplier for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving large amount of problems. Also, it provides a sequence which converges to the solution of the problem without discretization of the variables. In this study, an idea is proposed that accelerates the convergence of the sequence which results from the variational iteration formula for solving systems of delay differential equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Solving a class of nonlinear optimal control problems via he’s variational iteration method

Cited by 25 publications

References 10 publications

Solving A Class Of Nonlinear Optimal Control Problems By Differential Transformation Method

Solving A Class Of Nonlinear Optimal Control Problems By Differential Transformation Method

Approximating the Solution of Optimal Control Problems by Fuzzy Systems

Solution of linear time-varying multi-delay systems via variational iteration method

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