Convergence rate for a Gauss collocation method applied to unconstrained optimal control
Optimization and Control
2016-07-12 v3
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.
Cite
@article{arxiv.1507.08263,
title = {Convergence rate for a Gauss collocation method applied to unconstrained optimal control},
author = {William W. Hager and Hongyan Hou and Anil V. Rao},
journal= {arXiv preprint arXiv:1507.08263},
year = {2016}
}