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

William W. Hager (), Hongyan Hou () and Anil V. Rao ()
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William W. Hager: University of Florida
Hongyan Hou: Carnegie Mellon University
Anil V. Rao: University of Florida

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 6, 824 pages

Abstract: 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.

Keywords: Gauss collocation method; Convergence rate; Optimal control; Orthogonal collocation; 49M25; 49M37; 65K05; 90C30 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-016-0929-7

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