A mixed-integer framework for analyzing neural network-based controllers for piecewise affine systems with bounded disturbances

We present a method for representing the closed-loop dynamics of piecewise affine (PWA) systems with bounded additive disturbances and neural network-based controllers as mixed-integer (MI) linear constraints. We show that such representations enable the computation of robustly positively invariant (RPI) sets for the specified system class by solving MI linear programs. These RPI sets can subsequently be used to certify stability and constraint satisfaction. Furthermore, the approach allows to handle non-linear systems based on suitable PWA approximations and corresponding error bounds, which can be interpreted as the bounded disturbances from above.