Offset-free setpoint tracking using neural network controllers
This work provides stability guarantees for neural network controllers in setpoint tracking, which is important for safety-critical control systems.
This paper analyzes the local and global stability of offset-free setpoint tracking using neural network controllers, providing ellipsoidal inner approximations of the region of attraction. The method was demonstrated by verifying stability and offset-free tracking for a neural network controller trained to stabilize a linearized inverted pendulum.
In this paper, we present a method to analyze local and global stability in offset-free setpoint tracking using neural network controllers and we provide ellipsoidal inner approximations of the corresponding region of attraction. We consider a feedback interconnection of a linear plant in connection with a neural network controller and an integrator, which allows for offset-free tracking of a desired piecewise constant reference that enters the controller as an external input. Exploiting the fact that activation functions used in neural networks are slope-restricted, we derive linear matrix inequalities to verify stability using Lyapunov theory. After stating a global stability result, we present less conservative local stability conditions (i) for a given reference and (ii) for any reference from a certain set. The latter result even enables guaranteed tracking under setpoint changes using a reference governor which can lead to a significant increase of the region of attraction. Finally, we demonstrate the applicability of our analysis by verifying stability and offset-free tracking of a neural network controller that was trained to stabilize a linearized inverted pendulum.