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A reliable numerical approach for nonlinear fractional optimal control problems
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Abstract
In 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.
Title: A reliable numerical approach for nonlinear fractional optimal control problems
Description:
Abstract
In 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.
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