TY - GEN A1 - Casas, Eduardo A1 - Wachsmuth, Daniel A1 - Wachsmuth, Gerd T1 - Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems T2 - SIAM Journal on Control and Optimization (SICON) N2 - 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. KW - bang-bang control KW - bilinear controls KW - second-order conditions KW - sufficient optimality conditions KW - error analysis Y1 - 2018 U6 - https://doi.org/10.1137/17M1139953 SN - 0363-0129 SN - 1095-7138 VL - 56 IS - 6 SP - 4203 EP - 4227 ER -