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Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control

Author

Listed:
  • William W. Hager

    (University of Florida)

  • Hongyan Hou

    (Carnegie Mellon University)

  • Anil V. Rao

    (University of Florida)

Abstract

A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the number of collocation points increases, the discrete solution converges to the continuous solution at the collocation points, exponentially fast in the sup-norm. Numerical examples illustrating the convergence theory are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-016-0929-7
    DOI: 10.1007/s10957-016-0929-7
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    Cited by:

    1. 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.
    2. Elisha R. Pager & Anil V. Rao, 2022. "Method for solving bang-bang and singular optimal control problems using adaptive Radau collocation," Computational Optimization and Applications, Springer, vol. 81(3), pages 857-887, April.
    3. 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.
    4. 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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