Convergence rate for a Gauss collocation method applied to constrained optimal control
Numerical Analysis
2018-09-17 v4
Abstract
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for problems whose optimal state and costate possess two square integrable derivatives. The convergence theory is based on a stability result for the sup-norm change in the solution of a variational inequality relative to a 2-norm perturbation, and on a Sobolev space bound for the error in interpolation at the Gauss quadrature points and the additional point -1. The tightness of the convergence theory is examined using a numerical example.
Cite
@article{arxiv.1607.02798,
title = {Convergence rate for a Gauss collocation method applied to constrained optimal control},
author = {William W. Hager and Jun Liu and Subhashree Mohapatra and Anil V. Rao and Xiang-Sheng Wang},
journal= {arXiv preprint arXiv:1607.02798},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1605.02121