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

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

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Article ID: iaor20162414
Volume: 169
Issue: 3
Start Page Number: 801
End Page Number: 824
Publication Date: Jun 2016
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: optimization, programming: convex
Abstract:

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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