Regularization and implicit Euler discretization of linear-quadratic optimal control problems with bang-bang solutions
Regularization and implicit Euler discretization of linear-quadratic optimal control problems with bang-bang solutions
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DOI：
10.1016/j.amc.2016.04.028
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发表时间：
2016-09-05
影响因子：
4
通讯作者：
Seydenschwanz, Martin
中科院分区：
文献类型：
--
作者：
Alt, Walter;Schneider, Christopher;Seydenschwanz, Martin
We analyze the implicit Euler discretization for a class of convex linear-quadratic optimal control problems with control appearing linearly. Constraints are defined by lower and upper bounds for the controls, and the cost functional may depend on a regularization parameter.. Without any structural assumption on the optimal control we prove convergence of order 1 w.r.t. the mesh size for the discrete optimal values. Under the additional assumption that the optimal control is of bang-bang type and the switching function satisfies a growth condition around their zeros we show that the solutions are calm functions of perturbation and regularization parameters. By applying this result to the implicit Euler discretization we improve existing error estimates for discretizations based on the explicit Euler method. Numerical experiments confirm the theoretical findings and demonstrate the usefulness of implicit methods and regularization in case of bang-bang controls. (C) 2016 Elsevier Inc. All rights reserved.
