A numerical approach based on fractional-order hybrid functions of block-pulse and Bernoulli polynomials for numerical solutions of fractional optimal control problems

2021 ◽  
Author(s):  
O. Postavaru ◽  
A. Toma
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Bernoulli Polynomials ◽  
Numerical Approach ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Hybrid Functions ◽  
Fractional Optimal Control Problems

Shifted Chebyshev schemes for solving fractional optimal control problems

2019 ◽  
Vol 25 (15) ◽  
pp. 2143-2150 ◽  
Author(s):  
M Abdelhakem ◽  
H Moussa ◽  
D Baleanu ◽  
M El-Kady
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Numerical Examples ◽  
Fractional Optimal Control ◽  
Functional Approximation ◽  
Fractional Optimal Control Problems

Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.

Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach

SeMA Journal ◽  
2017 ◽  
Vol 74 (4) ◽  
pp. 585-603 ◽  
Author(s):  
Samaneh Soradi Zeid ◽  
Ali Vahidian Kamyad ◽  
Sohrab Effati ◽  
Seyed Ali Rakhshan ◽  
Soleiman Hosseinpour
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fixed Point Approach ◽  
Fractional Optimal Control Problems

A reliable numerical approach for nonlinear fractional optimal control problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Harendra Singh ◽  
Rajesh K. Pandey ◽  
Devendra Kumar
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Jacobi Polynomials ◽  
Operational Matrix ◽  
Numerical Approach ◽  
Numerical Results ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Special Cases ◽  
Fractional Optimal Control Problems

AbstractIn this work, we study a numerical approach for studying a nonlinear model of fractional optimal control problems (FOCPs). We have taken the fractional derivative in a dynamical system of FOCPs, which is in Liouville–Caputo sense. The presented scheme is a grouping of an operational matrix of integrations for Jacobi polynomials and the Ritz method. The proposed approach converts the FOCP into a system of nonlinear algebraic equations, which significantly simplify the problem. Convergence analysis of the scheme is also provided. The presented method is verified on the two illustrative examples to show its accuracy and applicability. Distinct special cases of Jacobi polynomials are considered as a basis to solve the FOCPs for comparison purpose. Further, tables and figures are employed to demonstrate the derived numerical results. The numerical results by the present method are also compared with some other techniques.

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.

Fractional-order Boubaker functions and their applications in solving delay fractional optimal control problems

2017 ◽  
Vol 24 (15) ◽  
pp. 3370-3383 ◽  
Author(s):  
Kobra Rabiei ◽  
Yadollah Ordokhani ◽  
Esmaeil Babolian
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Operational Matrix ◽  
Nonlinear Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Newton’S Iterative Method ◽  
Quadratic Performance ◽  
Fractional Optimal Control Problems

In this paper, a new set of functions called fractional-order Boubaker functions is defined for solving the delay fractional optimal control problems with a quadratic performance index. To solve the problem, first we obtain the operational matrix of the Caputo fractional derivative of these functions and the operational matrix of multiplication to solve the nonlinear problems for the first time. Also, a general formulation for the delay operational matrix of these functions has been achieved. Then we utilized these matrices to solve delay fractional optimal control problems directly. In fact, the delay fractional optimal control problem converts to an optimization problem, which can then be easily solved with the aid of the Gauss–Legendre integration formula and Newton’s iterative method. Convergence of the algorithm is proved. The applicability of the method is shown by some examples; moreover, a comparison with the existing results shows the preference of this method.

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