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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Bibliographic Details
Published in:Nonlinear dynamics Vol. 108; no. 1; pp. 265 - 277
Main Authors: Ghanbari, Ghodsieh, Razzaghi, Mohsen
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2022
Springer Nature B.V
Subjects:
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
Beta function
Numerical method
Distributed-order fractional optimal control
Fractional-order Chebyshev wavelet
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary: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.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-07195-4