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Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

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Abstract

This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to canonical constraints, where the fractional-order derivatives are expressed in the Caputo sense. To solve the problem by discretization scheme, an explicit numerical integration technique is proposed for solving the fractional-order system, and the trapezoidal rule is introduced to approximate the cost functional. Then, the gradients of the resulting cost and constraint functions are derived. On the basis of this result, we develop a gradient-based optimization algorithm to numerically solve the discretized problem. Finally, numerical results of several non-trivial examples are provided to illustrate the applicability and effectiveness of the proposed algorithm.

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Acknowledgements

The first author is supported by the National Natural Science Foundation of China (Grant No. 11771008). The second author is supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019MA031). The third and fourth authors are supported by the Australian Research Council (Discovery Grant DP190103361).

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Correspondence to Zhaohua Gong.

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Communicated by Qamrul Hasan Ansari.

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Liu, C., Gong, Z., Teo, K.L. et al. Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays. J Optim Theory Appl 193, 856–876 (2022). https://doi.org/10.1007/s10957-021-01935-7

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