Journal
JOURNAL OF VIBRATION AND CONTROL
Volume 19, Issue 16, Pages 2523-2540Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1077546312458308
Keywords
Bernstein polynomials; Caputo derivative; fractional optimal control problems; operational matrix
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In this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.
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