  This work considers artificial feed-forward neural networks as parametric
approximators in optimal control of discrete-time systems. Two different
approaches are introduced to take polytopic input constraints into account. The
first approach determines (sub-)optimal inputs by the application of gradient
methods. Closed-form expressions for the gradient of general neural networks
with respect to their inputs are derived. The approach allows to consider
state-dependent input constraints, as well as to ensure the satisfaction of
state constraints by exploiting recursive reachable set computations. The
second approach makes use of neural networks with softmax output units to map
states into parameters, which determine (sub-)optimal inputs by a convex
combination of the vertices of the input constraint set. The application of
both approaches in model predictive control is discussed, and results obtained
for a numerical example are used for illustration.
