A gradient-based optimization algorithm to solve optimal control problems with conformable fractional-order derivatives

In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discr...

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Vydáno v:Journal of computational and applied mathematics Ročník 454; s. 116169
Hlavní autoři: Gong, Zhaohua, Liu, Chongyang, Teo, Kok Lay, Wu, Yonghong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 15.01.2025
Témata:
Conformable fractional derivative
Numerical integration
Numerical optimization
Optimal control
Numerical integration
Numerical optimization
Optimal control
Conformable fractional derivative
ISSN:0377-0427
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Shrnutí:In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discretization method for the governed fractional-order system as well as the cost and constraint functionals, which yields a discretized approximate problem. We further derive the gradients of the cost and constraint functionals in regard to the discretized controls. On the basis of this result, a numerical optimization approach to solve the approximate problem is developed. Finally, three non-trivial example problems are solved to illustrate the applicability and effectiveness of the developed approach.
ISSN:0377-0427
DOI:10.1016/j.cam.2024.116169