Exact representation of piecewise affine functions via neural networks

Piecewise affine (PWA) control laws often arise in automatic control. A popular example is explicit model predictive control (MPC). On the other hand, it is well known that artificial neural neutworks (ANNs) with rectifier or maxout activations lead to PWA input-output relations. Against this background, it is natural to investigate whether ANNs can be parametrized in such a way that they exactly reproduce the input-output relation of a given PWA function, e.g., a given explicit MPC law. We briefly summarize a known but numerically demanding approach based on maxout networks and provide a novel and efficient method using rectifier networks for the special case of one-dimensional inputs.