  Neural network (NN) approximations of model predictive control (MPC) are a
versatile approach if the online solution of the underlying optimal control
problem (OCP) is too demanding and if an exact computation of the explicit MPC
law is intractable. The drawback of such approximations is that they typically
do not preserve stability and performance guarantees of the original MPC.
However, such guarantees can be recovered if the maximum error with respect to
the optimal control law and the Lipschitz constant of that error are known. We
show in this work how to compute both values exactly when the control law is
approximated by a maxout NN. We build upon related results for ReLU NN
approximations and derive mixed-integer (MI) linear constraints that allow a
computation of the output and the local gain of a maxout NN by solving an MI
feasibility problem. Furthermore, we show theoretically and experimentally that
maxout NN exist for which the maximum error is zero.
