Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems.

Shifted Legendre orthonormal polynomials (SLOPs) are used to approximate the numerical solutions of fractional optimal control problems. To do so, first, the operational matrix of the Caputo fractional derivative, the SLOPs, and Lagrange multipliers are used to convert such problems into algebraic equations. Also, the method is proposed for solving multidimensional problems, and its convergence is proved. This method is tested on some nonlinear examples. The results indicate that the technique can efficiently solve multidimensional problems. [ABSTRACT FROM AUTHOR]