Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations

In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a f...

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Bibliographic Details
Published in:Journal of vibration and control 2023-03, Vol.29 (5-6), p.1164-1175
Main Authors: Heydari, Mohammad Hossein, Razzaghi, Mohsen, Avazzadeh, Zakieh
Format: Article
Language:English
Subjects:
Algorithms
Basis functions
Differential equations
Fractional calculus
Lagrange multiplier
Mathematical analysis
Mathematical programming
Optimal control
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Summary:In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a fractional integro-differential equation. The presented technique is based on the expressed basis functions and their fractional integral matrix together with the Gauss–Legendre integration method and the Lagrange multipliers algorithm. This approach converts the original problem into a mathematical programming one. Three examples are investigated numerically to verify the capability and reliability of the approach.
ISSN:1077-5463
1741-2986
DOI:10.1177/10775463211059364