Convergence Rate for a Radau hp Collocation Method Applied to Constrained Optimal Control

摘要: For unconstrained control problems, a local convergence rate is established for an $hp$-method based on collocation at the Radau quadrature points in each mesh interval of discretization. If continuous problem has sufficiently smooth solution and Hamiltonian satisfies strong convexity condition, then discrete possesses minimizer neighborhood solution, as either number or intervals increase, convergences to sup-norm. The exponentially fast with respect degree polynomials interval, while error bounded by polynomial spacing. An advantage $hp$-scheme over global that there guarantee when small, result requires norm linearized dynamics small. Numerical examples explore theory.