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Bounds for integration matrices that arise in Gauss and Radau collocation

Author

Listed:
  • Wanchun Chen

    (Beihang University)

  • Wenhao Du

    (Beihang University)

  • William W. Hager

    (University of Florida)

  • Liang Yang

    (Beihang University)

Abstract

Bounds are established for integration matrices that arise in the convergence analysis of discrete approximations to optimal control problems based on orthogonal collocation. Weighted Euclidean norm bounds are derived for both Gauss and Radau integration matrices; these weighted norm bounds yield sup-norm bounds in the error analysis.

Suggested Citation

  • Wanchun Chen & Wenhao Du & William W. Hager & Liang Yang, 2019. "Bounds for integration matrices that arise in Gauss and Radau collocation," Computational Optimization and Applications, Springer, vol. 74(1), pages 259-273, September.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00099-5
    DOI: 10.1007/s10589-019-00099-5
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    References listed on IDEAS

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    1. William W. Hager & Hongyan Hou & Subhashree Mohapatra & Anil V. Rao & Xiang-Sheng Wang, 2019. "Correction to: Convergence rate for a Radau hp collocation method applied to constrained optimal control," Computational Optimization and Applications, Springer, vol. 74(1), pages 315-316, September.
    2. William W. Hager & Hongyan Hou & Subhashree Mohapatra & Anil V. Rao & Xiang-Sheng Wang, 2019. "Convergence rate for a Radau hp collocation method applied to constrained optimal control," Computational Optimization and Applications, Springer, vol. 74(1), pages 275-314, September.
    3. William W. Hager & Hongyan Hou & Anil V. Rao, 2016. "Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 801-824, June.
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    Cited by:

    1. William W. Hager & Hongyan Hou & Subhashree Mohapatra & Anil V. Rao & Xiang-Sheng Wang, 2019. "Convergence rate for a Radau hp collocation method applied to constrained optimal control," Computational Optimization and Applications, Springer, vol. 74(1), pages 275-314, September.
    2. Joseph D. Eide & William W. Hager & Anil V. Rao, 2021. "Modified Legendre–Gauss–Radau Collocation Method for Optimal Control Problems with Nonsmooth Solutions," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 600-633, December.

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