Transformed orthogonal functions for solving infinite horizon fractional optimal control problems

In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal con-trol problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear pro-gramming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved. In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal con-trol problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear pro-gramming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved.