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Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices. (English) Zbl 1358.93097
Summary: 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.

MSC:
93C23 Control/observation systems governed by functional-differential equations
26A33 Fractional derivatives and integrals
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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