%0 Journal Article %T Solution of Fractional Optimal Control Problems with Noise Function Using the Bernstein Functions %J Control and Optimization in Applied Mathematics %I Payame Noor University (PNU) %Z 2383-3130 %A Nemati, Ali %A Alizadeh, Ali %A Soltanian, Fahime %D 2019 %\ 07/01/2019 %V 4 %N 1 %P 37-51 %! Solution of Fractional Optimal Control Problems with Noise Function Using the Bernstein Functions %K Optimization‎ %K ‎Spectral method‎ %K ‎Noise function‎ %K ‎Fractional optimal control‎ %K ‎Operational matrix %R 10.30473/coam.2020.33909.1078 %X This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method‎. ‎The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions‎. ‎By substituting these estimated functions into the cost functional‎, ‎an unconstrained nonlinear optimization problem is achieved‎. In order to solve this optimization problem‎, ‎the Matlab software and its optimization toolbox are used‎. ‎In the considered FOCP‎, ‎the performance index is expressed as a function of both state and control functions‎. ‎The method is robust enough because of its computational consistency in the presence of the noise function‎. ‎Moreover‎, ‎the proposed scheme has a good pliability satisfying the given initial and boundary conditions‎. ‎At last‎, ‎some test problems are investigated to confirm the efficiency and applicability of the new method. %U https://mathco.journals.pnu.ac.ir/article_7150_b65ba1ebf0b4b4894ac8ba04ae5f4b45.pdf