In Proximity of ReLU DNN, PWA Function, and Explicit MPC
This work addresses the connection between neural networks and control theory, potentially enabling more efficient MPC implementations, but it appears incremental as it builds on existing analyses of ReLU DNNs and PWA functions.
The paper investigates the relationship between ReLU deep neural networks (DNNs) and piecewise affine (PWA) functions, focusing on representing explicit model predictive control (MPC) policies as ReLU DNNs and vice versa. It develops an approximate method for identifying input-space in ReLU nets to derive PWA functions and studies inverse multiparametric programs for reconstructing constraints and cost functions from PWA functions.
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.