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arXiv · 1508.03783

Convergence rate for a Radau 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 Radau 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. An earlier paper analyzes an orthogonal collocation method based on Gauss quadrature, where neither end point of the problem domain is a collocation point. For the Radau quadrature scheme, one end point is a collocation point.

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William W. Hager, Hongyan Hou, Anil V. Rao. 2015-08-16. Convergence rate for a Radau collocation method applied to unconstrained optimal control. https://arxiv.org/abs/1508.03783

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