A mixed-integer framework for analyzing neural network-based controllers for piecewise affine systems with bounded disturbances
For control engineers, this provides a formal verification method for neural network-controlled systems with bounded disturbances, though it is incremental as it extends existing mixed-integer techniques to a specific system class.
The paper presents a mixed-integer framework to compute robustly positively invariant sets for piecewise affine systems with bounded disturbances and neural network controllers, enabling certification of stability and constraint satisfaction.
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.