Ultraspherical Integral Method for Optimal Control Problems Governed by Ordinary Differential Equations

Authors:
H. M. El-Hawary;M. S. Salim;H. S. Hussien
Affiliations:
Department of Mathematics, Faculty of Science, Assuit University, Assuit, Egypt. (E-mail: elhawary@aun.eun.eg)/;Department of Mathematics, Faculty of Science, El-Azhar University, Assuit, Egypt/;Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt. (E-mail: s.hussien@mailcity.com)
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

In this paper an ultraspherical integral method is proposed to solve optimal control problems governed by ordinary differential equations. Ultraspherical approximation method reduced the problem to a constrained optimization problem. Penalty leap frog method is presented to solve the resulting constrained optimization problem. Error estimates for the ultraspherical approximations are derived and a technique that gives an optimal approximation of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.