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 · SIAM Journal on Control and Optimization · 2018
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.