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

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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.

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Acknowledgements

The support of the National Natural Science Foundation of China (Grants 12271307 and 12271335) and the Fundamental Research Grant Scheme of Malaysia (Grant FRGS/1/2021/STG06/SYUC/03/1) is acknowledged.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shandong Technology and Business University, Yantai, 264005, China

    Chongyang Liu & Zhaohua Gong

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Changjun Yu

  3. School of Mathematical Sciences, Sunway University, 47500, Kuala Lumpur, Malaysia

    Huey Tyng Cheong & Kok Lay Teo

Authors
  1. Chongyang Liu
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  2. Changjun Yu
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  3. Zhaohua Gong
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  4. Huey Tyng Cheong
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Correspondence to Chongyang Liu.

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Communicated by Jen-Chih Yao.

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Liu, C., Yu, C., Gong, Z. et al. Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives. J Optim Theory Appl 197, 798–816 (2023). https://doi.org/10.1007/s10957-023-02212-5

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