Numerical solutions for distributed-order fractional optimal control problems by using generalized fractional-order Chebyshev wavelets

This paper studies a numerical approach based on generalized fractional-order Chebyshev wavelets for solving distributed-order fractional optimal control problems (DO-FOCPs). The exact value of the Riemann–Liouville fractional integral operator of the given wavelets is computed by applying regulariz...

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Vydané v:Nonlinear dynamics Ročník 108; číslo 1; s. 265 - 277
Hlavní autori: Ghanbari, Ghodsieh, Razzaghi, Mohsen
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht Springer Netherlands 01.03.2022
Springer Nature B.V
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Abstract This paper studies a numerical approach based on generalized fractional-order Chebyshev wavelets for solving distributed-order fractional optimal control problems (DO-FOCPs). The exact value of the Riemann–Liouville fractional integral operator of the given wavelets is computed by applying regularized beta function. The exact formula and collocation method are applied to transform the DO-FOCP to a new optimization problem. This new problem can be solved by the existing methods. Four examples are given to show the advantage of this method in comparison with the existing methods in the literature.
AbstractList This paper studies a numerical approach based on generalized fractional-order Chebyshev wavelets for solving distributed-order fractional optimal control problems (DO-FOCPs). The exact value of the Riemann–Liouville fractional integral operator of the given wavelets is computed by applying regularized beta function. The exact formula and collocation method are applied to transform the DO-FOCP to a new optimization problem. This new problem can be solved by the existing methods. Four examples are given to show the advantage of this method in comparison with the existing methods in the literature.
Author Razzaghi, Mohsen
Ghanbari, Ghodsieh
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  surname: Razzaghi
  fullname: Razzaghi, Mohsen
  email: razzaghi@math.msstate.edu
  organization: Department of Mathematics and Statistics, Mississippi State University
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Distributed-order fractional optimal control
Fractional-order Chebyshev wavelet
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Snippet This paper studies a numerical approach based on generalized fractional-order Chebyshev wavelets for solving distributed-order fractional optimal control...
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SubjectTerms Approximation
Automotive Engineering
Chebyshev approximation
Classical Mechanics
Collocation methods
Control
Control theory
Dynamical Systems
Engineering
Fractional calculus
Mathematical functions
Mechanical Engineering
Operators (mathematics)
Optimal control
Optimization
Original Paper
Vibration
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Title Numerical solutions for distributed-order fractional optimal control problems by using generalized fractional-order Chebyshev wavelets
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