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A Legendre Galerkin spectral method for optimal control problems

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Abstract

This paper considers the Legendre Galerkin spectral approximation for the unconstrained optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yanping Chen

  2. The Faculty of Mathematics, Chengyi College, Jimei University, Xiamen, 361021, China

    Nianshi Xia

  3. Hunan Key Laboratory for Computation and Simulation in Science and Engineering; School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Nianyu Yi

Authors
  1. Yanping Chen
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  2. Nianshi Xia
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  3. Nianyu Yi
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Corresponding author

Correspondence to Yanping Chen.

Additional information

This work is supported by the Foundation for Talent Introduction of Guangdong Provincial University, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), and the National Natural Science Foundation of China under Grant No. 10971074.

This paper was recommended for publication by Editor Ningning YAN.

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Chen, Y., Xia, N. & Yi, N. A Legendre Galerkin spectral method for optimal control problems. J Syst Sci Complex 24, 663–671 (2011). https://doi.org/10.1007/s11424-011-8016-5

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  • DOI: https://doi.org/10.1007/s11424-011-8016-5

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