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

Chongyang Liu (), Zhaohua Gong (), Kok Lay Teo () and Song Wang ()
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Chongyang Liu: Shandong Technology and Business University
Zhaohua Gong: Shandong Technology and Business University
Kok Lay Teo: Sunway University
Song Wang: Curtin University

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 35, 856-876

Abstract: 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.

Keywords: Fractional-order system; Time-varying delay; Optimal control; Discretization scheme; Gradient computation; 34K37; 49M37; 90C55 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01935-7

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