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arXiv · 1707.06880

Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems

Eduardo Casas·Daniel Wachsmuth·Gerd Wachsmuth
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Abstract

We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in $L^1$. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization, and prove error estimates of bang-bang controls in $L^1$-norms.

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Eduardo Casas, Daniel Wachsmuth, Gerd Wachsmuth. 2017-07-21. Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems. https://arxiv.org/abs/1707.06880

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