A semidefinite programming approach for solving fractional optimal control problems. (3rd July 2017)

• Record Type: Journal Article
• Authors: Dehghan, R.; Keyanpour, M.
• Is Part Of: Optimization. Volume 66:Number 7(2017)
• Page Start: 1157
• Page End: 1176
• Publication Date: 2017-07-03
• Subjects: Method of moments -- fractional derivative -- optimal control -- semidefinite programming -- optimization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1316501
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: This paper presents a numerical scheme for solving fractional optimal control. The fractional derivative in this problem is in the Riemann–Liouville sense. The proposed method, based upon the method of moments, converts the fractional optimal control problem to a semidefinite optimization problem; namely, the nonlinear optimal control problem is converted to a convex optimization problem. The Grunwald–Letnikov formula is also used as an approximation for fractional derivative. The solution of fractional optimal control problem is found by solving the semidefinite optimization problem. Finally, numerical examples are presented to show the performance of the method.