Physics-guided neural networks for feedforward control with input-to-state stability guarantees

The increasing demand on precision and throughput within high-precision mechatronics industries requires a new generation of feedforward controllers with higher accuracy than existing, physics-based feedforward controllers. As neural networks are universal approximators, they can in principle yield feedforward controllers with a higher accuracy, but suffer from bad extrapolation outside the training data set, which makes them unsafe for implementation in industry. Motivated by this, we develop a novel physics-guided neural network (PGNN) architecture that structurally merges a physics-based layer and a black-box neural layer in a single model. The parameters of the two layers are simultaneously identified, while a novel regularization cost function is used to prevent competition among layers and to preserve consistency of the physics-based parameters. Moreover, in order to ensure stability of PGNN feedforward controllers, we develop sufficient conditions for analyzing or imposing (during training) input-to-state stability of PGNNs, based on novel, less conservative Lipschitz bounds for neural networks. The developed PGNN feedforward control framework is validated on a real-life, high-precision industrial linear motor used in lithography machines, where it reaches a factor 2 improvement with respect to physics-based mass-friction feedforward and it significantly outperforms alternative neural network based feedforward controllers.