Convergence rate for a Radau collocation method applied to unconstrained optimal control
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.
Cite
@article{arxiv.1508.03783,
title = {Convergence rate for a Radau collocation method applied to unconstrained optimal control},
author = {William W. Hager and Hongyan Hou and Anil V. Rao},
journal= {arXiv preprint arXiv:1508.03783},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1507.08263