  Rectifier (ReLU) deep neural networks (DNN) and their connection with
piecewise affine (PWA) functions is analyzed. The paper is an effort to find
and study the possibility of representing explicit state feedback policy of
model predictive control (MPC) as a ReLU DNN, and vice versa. The complexity
and architecture of DNN has been examined through some theorems and
discussions. An approximate method has been developed for identification of
input-space in ReLU net which results a PWA function over polyhedral regions.
Also, inverse multiparametric linear or quadratic programs (mp-LP or mp-QP) has
been studied which deals with reconstruction of constraints and cost function
given a PWA function.
