JournalArticlemarkolf2023dnnapproximationsDNN-Approximations of Control Laws for Nonlinear Systems with Polytopic Constraints.2023MarkolfL.StursbergO.Proc. of the 22nd IFAC World CongressThis work focuses on deep artificial feed-forward neural networks as parametric function approximators in optimal control of discrete-time nonlinear but affine-in-control systems subject to polytopic constraints on the continuous states and control inputs. The neural networks are either considered as approximators of optimal control laws or as approximators of the corresponding cost functions. In both cases, an approach is developed for determining the approximated optimal control inputs without violating the constraints. A simple approximate policy iteration algorithm exploiting both approaches is finally presented and illustrated for a numerical example.control, isac-www