Title: A convergence computational scheme for optimal control problems governed by Schrödinger equations

Authors: Akbar Hashemi Borzabadi; Mohammad Heidari

Addresses: School of Mathematics and Computer Science, Damghan University, Damghan, Iran ' School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Abstract: In this paper, a numerical scheme for obtaining approximate solutions of optimal control problems governed by Schrödinger equations is presented. In this method, by considering a partition of the control space, discrete form of the problem is converted to a quasi assignment problem. Then using an evolutionary algorithm, approximate optimal control is obtained as a piecewise linear function. The comparison between the numerical solution and the exact solution for the test cases shows the good accuracy of the presented method.

Keywords: optimal control; Schrödinger equations; evolutionary algorithms; discretisation; approximation; convergence computing.

DOI: 10.1504/IJMMNO.2013.055198

International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.2, pp.91 - 102

Received: 03 Sep 2012
Accepted: 05 Jan 2013

Published online: 22 Jul 2013 *

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