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

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...

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Vydané v:Journal of optimization theory and applications Ročník 197; číslo 2; s. 798 - 816
Hlavní autori: Liu, Chongyang, Yu, Changjun, Gong, Zhaohua, Cheong, Huey Tyng, Teo, Kok Lay
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.05.2023
Springer Nature B.V
Predmet:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Discretization
Engineering
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Numerical integration
Operations Research/Decision Theory
Optimal control
Optimization
Optimization algorithms
Optimization techniques
Polynomials
Theory of Computation
Fractional optimal control
Atangana–Baleanu derivative
Optimization algorithm
90C55
34K37
49M37
Discretization scheme
ISSN:0022-3239, 1573-2878
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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.
AbstractList 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.
Author Gong, Zhaohua
Cheong, Huey Tyng
Liu, Chongyang
Yu, Changjun
Teo, Kok Lay
Author_xml – sequence: 1
  givenname: Chongyang
  orcidid: 0000-0002-2229-6717
  surname: Liu
  fullname: Liu, Chongyang
  email: chongyangliu@aliyun.com
  organization: School of Mathematics and Information Science, Shandong Technology and Business University
– sequence: 2
  givenname: Changjun
  surname: Yu
  fullname: Yu, Changjun
  organization: Department of Mathematics, Shanghai University
– sequence: 3
  givenname: Zhaohua
  surname: Gong
  fullname: Gong, Zhaohua
  organization: School of Mathematics and Information Science, Shandong Technology and Business University
– sequence: 4
  givenname: Huey Tyng
  surname: Cheong
  fullname: Cheong, Huey Tyng
  organization: School of Mathematical Sciences, Sunway University
– sequence: 5
  givenname: Kok Lay
  surname: Teo
  fullname: Teo, Kok Lay
  organization: School of Mathematical Sciences, Sunway University
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Keywords Fractional optimal control
Atangana–Baleanu derivative
Optimization algorithm
90C55
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Discretization scheme
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SubjectTerms Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Discretization
Engineering
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Numerical integration
Operations Research/Decision Theory
Optimal control
Optimization
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Theory of Computation
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Title Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives
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