Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives

In this paper, a computational method is proposed for solving a class of fractional optimal control problems subject to canonical constraints of equality and inequality. Fractional derivatives are described in the Atangana–Baleanu-Caputo sense, and their fractional orders can be different. To solve...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 197; no. 2; pp. 798 - 816
Main Authors: Liu, Chongyang, Yu, Changjun, Gong, Zhaohua, Cheong, Huey Tyng, Teo, Kok Lay
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2023
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Discretization
Engineering
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Numerical integration
Operations Research/Decision Theory
Optimal control
Optimization
Optimization algorithms
Optimization techniques
Polynomials
Theory of Computation
Fractional optimal control
Atangana–Baleanu derivative
Optimization algorithm
90C55
34K37
49M37
Discretization scheme
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, a computational method is proposed for solving a class of fractional optimal control problems subject to canonical constraints of equality and inequality. Fractional derivatives are described in the Atangana–Baleanu-Caputo sense, and their fractional orders can be different. To solve this problem, we present a discretization scheme based on the trapezoidal rule and a novel numerical integration technique. Then, the gradient formulas of the cost and constraint functions with respect to the decision variables are derived. Furthermore, a gradient-based optimization algorithm for solving the discretized optimal control problem is developed. Finally, the applicability and effectiveness of the proposed algorithm are verified through three non-trivial example problems.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02212-5