Abstract
We investigate Euler discretization for a class of optimal control problems with a nonlinear cost functional of Mayer type, a nonlinear system equation with control appearing linearly and constraints defined by lower and upper bounds for the controls. Under the assumption that the cost functional satisfies a growth condition we prove for the discrete solutions Hölder type error estimates w.r.t. the mesh size of the discretization. If a stronger second-order optimality condition is satisfied the order of convergence can be improved. Numerical experiments confirm the theoretical findings.
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The authors would like to thank the anonymous referees for their careful reading of the manuscript and their constructive and valuable suggestions and comments.
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Alt, W., Felgenhauer, U. & Seydenschwanz, M. Euler discretization for a class of nonlinear optimal control problems with control appearing linearly. Comput Optim Appl 69, 825–856 (2018). https://doi.org/10.1007/s10589-017-9969-7
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DOI: https://doi.org/10.1007/s10589-017-9969-7