The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems

2011 ◽  
Vol 17 (13) ◽  
pp. 2059-2065 ◽  
Author(s):  
SA Yousefi ◽  
A Lotfi ◽  
M Dehghan
Keyword(s):  
Optimal Control ◽  
Exact Solution ◽  
Approximate Solution ◽  
Collocation Method ◽  
Algebraic System ◽  
Optimal Control Problems ◽  
New Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

In this article the Legendre multiwavelet basis with the aid of a collocation method has been applied to give the approximate solution for the fractional optimal control problems (FOCPs). The properties of the Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of an algebraic system. Numerical results and a comparison with the exact solution in the cases when we have an exact solution are given to demonstrate the applicability and efficiency of the new method.

A numerical approach for solving fractional optimal control problems with mittag-leffler kernel

2021 ◽  
pp. 107754632110169
Author(s):  
Hossein Jafari ◽  
Roghayeh M Ganji ◽  
Khosro Sayevand ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Approximate Solution ◽  
Optimal Control Problems ◽  
Fractional Integration ◽  
Numerical Approach ◽  
Control Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana–Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.

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