Convergence rate for a Gauss collocation method applied to constrained optimal control

Abstract

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.

arXiv commentarXiv admin note: text overlap with arXiv:1605.02121

References in corpus (1)

• Convergence rate for a Gauss collocation method applied to unconstrained optimal control

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