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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assuit University, Assuit, Egypt

    H.M. El-Hawary

  2. El-Azhar University, Assuit, Egypt

    M.S. Salim

  3. Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

    H.S. Hussien

Authors
  1. H.M. El-Hawary
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  2. M.S. Salim
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  3. H.S. Hussien
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El-Hawary, H., Salim, M. & Hussien, H. Ultraspherical Integral Method for Optimal Control Problems Governed by Ordinary Differential Equations. Journal of Global Optimization 25, 283–303 (2003). https://doi.org/10.1023/A:1022463810376

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  • DOI: https://doi.org/10.1023/A:1022463810376

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