Discretization of semilinear bang-singular-bang control problems.

Bang-singular controls may appear in optimal control problems where the control enters the system linearly. We analyze a discretization of the first-order system of necessary optimality conditions written in terms of a variational inequality (or: inclusion) under appropriate assumptions including second-order optimality conditions. For the so-called semilinear case, it is proved that the discrete control has the same principal bang-singular-bang structure as the reference control and, in $$L_{1}$$ topology, the convergence is of order one w.r.t. the stepsize. [ABSTRACT FROM AUTHOR]