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A semidefinite programming approach for solving fractional optimal control problems
Authors:R Dehghan  M Keyanpour
Institution:1. Faculty of Mathematical Sciences, Department of Applied Mathematics, University of Guilan, Rasht, Iran.rdehghan110@gmail.com;3. Faculty of Mathematical Sciences, Department of Applied Mathematics, University of Guilan, Rasht, Iran.
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.
Keywords:Method of moments  fractional derivative  optimal control  semidefinite programming  optimization
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