Convergence rate for a Radau collocation method applied to unconstrained optimal control
Provides a theoretical convergence guarantee for a practical collocation method used in optimal control, extending prior analysis from Gauss to Radau quadrature.
The paper proves exponential convergence in the sup-norm for a Radau collocation method applied to unconstrained optimal control problems, provided the solution is smooth and the Hamiltonian is strongly convex.
A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently 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 convergences exponentially fast in the sup-norm to the continuous solution. An earlier paper analyzes an orthogonal collocation method based on Gauss quadrature, where neither end point of the problem domain is a collocation point. For the Radau quadrature scheme, one end point is a collocation point.