Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control

A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a 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 converges to the continuous solution at the collocation points, exponentially fast in the sup-norm. Numerical examples illustrating the convergence theory are provided.

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