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arXiv · 1607.02798

Convergence rate for a Gauss collocation method applied to constrained optimal control

William W. Hager·Jun Liu·Subhashree Mohapatra·Anil V. Rao·Xiang-Sheng Wang
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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.

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William W. Hager, Jun Liu, Subhashree Mohapatra, Anil V. Rao, Xiang-Sheng Wang. 2016-07-11. Convergence rate for a Gauss collocation method applied to constrained optimal control. https://doi.org/10.1137/16m1096761

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