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

2017/07/21 by Casas, Eduardo, Wachsmuth, Daniel, Wachsmuth, Gerd
#35J61 #49K20 #49K30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1707.06880

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 L¹. 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 L¹-norms.

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