State Parametrization Method Based on Shifted Legendre Polynomials for Solving Fractional Optimal Control Problems

In this paper, the parametric optimization method is used to solve a class of fractional optimal control problems. The solution is based on state parametrization, as a linear combination of shifted Legendre polynomials with unknown coefficients. An iterative algorithm is proposed for computing optimal coefficients. In this method the state and control variables can be approximated as a function of time. Convergence of the algorithm is investigated and to show the efficiency of the presented method three examples are solved and the results are compared with exact solution. © 2017, Springer (India) Private Ltd., part of Springer Nature.