Journal
JOURNAL OF VIBRATION AND CONTROL
Volume 29, Issue 5-6, Pages 1164-1175Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/10775463211059364
Keywords
Orthonormal piecewise Bernoulli functions; fractional optimal control problems; fractional integral matrix
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In this study, orthonormal piecewise Bernoulli functions are generated as new basis functions and an explicit matrix related to the fractional integration of these functions is obtained. A direct method is developed to solve a new set of optimal control problems defined using a fractional integro-differential equation.
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.
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