Abstract
This paper studies the local convergence properties of the control parameterization Ritz method in which the control variable is approximated over a finite-dimensional subspace. The nonlinear free-endpoint optimal control problem is considered, and error bounds are derived for both the cost functional and state-control convergence. Explicit error bounds are obtained for the particular case of approximations over spline spaces. On specializing the general results to the linear-quadratic regulator problem, global convergence results are obtained. Computational results supporting the theoretically derived error bounds are presented.
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Communicated by C. T. Leondes
This research was supported by the University Grants Committee of New Zealand.
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Sirisena, H.R., Chou, F.S. Convergence of the control parameterization Ritz method for nonlinear optimal control problems. J Optim Theory Appl 29, 369–382 (1979). https://doi.org/10.1007/BF00933141
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DOI: https://doi.org/10.1007/BF00933141