%0 Journal Article
%T Convergence rate for a Radau collocation method applied to unconstrained optimal control
%A William W. Hager
%A Hongyan Hou
%A Anil V. Rao
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1508.03783v3