Convergence rate for a Gauss collocation method applied to constrained   optimal control
  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. 
William W. Hager, Jun Liu, Subhashree Mohapatra, Anil V. Rao, and   Xiang-Sheng Wang
math.NA