A numerical technique for solving fractional optimal control problems

Authors:
A. Lotfi;Mehdi Dehghan;S. A. Yousefi
Affiliations:
Department of Mathematics, Shahid Beheshti University, G.C. Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;Department of Mathematics, Shahid Beheshti University, G.C. Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 2
Cited 2

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
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Abstract

This paper presents a numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. The method is based upon the Legendre orthonormal polynomial basis. The operational matrices of fractional Riemann-Liouville integration and multiplication, along with the Lagrange multiplier method for the constrained extremum are considered. By this method, the given optimization problem reduces to the problem of solving a system of algebraic equations. By solving this system, we achieve the solution of the FOCP. Illustrative examples are included to demonstrate the validity and applicability of the new technique.