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arXiv · 1507.08263

Convergence rate for a Gauss collocation method applied to unconstrained optimal control

William W. Hager·Hongyan Hou·Anil V. Rao
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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 sufficiently 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 convergences exponentially fast in the sup-norm to the continuous solution. This is the first convergence rate result for an orthogonal collocation method based on global polynomials applied to an optimal control problem.

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William W. Hager, Hongyan Hou, Anil V. Rao. 2015-08-16. Convergence rate for a Gauss collocation method applied to unconstrained optimal control. https://doi.org/10.1007/s10957-016-0929-7

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