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

Chongyang Liu (), Changjun Yu (), Zhaohua Gong (), Huey Tyng Cheong () and Kok Lay Teo ()
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Chongyang Liu: Shandong Technology and Business University
Changjun Yu: Shanghai University
Zhaohua Gong: Shandong Technology and Business University
Huey Tyng Cheong: Sunway University
Kok Lay Teo: Sunway University

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 2, No 14, 798-816

Abstract: Abstract 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.

Keywords: Fractional optimal control; Atangana–Baleanu derivative; Discretization scheme; Optimization algorithm; 34K37; 49M37; 90C55 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-023-02212-5

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