Abstract
We analyze a combined regularization–discretization approach for a class of linear-quadratic optimal control problems. By choosing the regularization parameter \(\alpha \) with respect to the mesh size \(h\) of the discretization we approximate the optimal bang–bang control. Under weaker assumptions on the structure of the switching function we generalize existing convergence results and prove error estimates of order \({\mathcal {O}}(h^{1/(k+1)})\) with respect to the controllability index \(k\).
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The author would like to thank the anonymous reviewers for their valuable comments.
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Seydenschwanz, M. Convergence results for the discrete regularization of linear-quadratic control problems with bang–bang solutions. Comput Optim Appl 61, 731–760 (2015). https://doi.org/10.1007/s10589-015-9730-z
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DOI: https://doi.org/10.1007/s10589-015-9730-z