Neural network training with persistence of excitation

In Project P1, we use systems and control theoretic concepts to develop and analyze novel methods for supervised training of neural networks (NNs) with generalization guarantees. Specifically, two different approaches are pursued. First, we leverage recent advances in the field of optimization-based estimation for nonlinear systems, in particular moving horizon estimation (MHE). Second, we exploit novel methods from the field of data-driven control, such as data-based representations of dynamical systems using Willems' fundamental lemma (FL).

The main objective is to further develop and use these tools to obtain generalization guarantees for the trained neural network. In particular, this entails that the difference between the outputs of the trained NN and of some NN with ideal weights is contained within specific error bounds. To this end, different notions of persistence of excitation (PE) and other data informativity conditions will be studied. Moreover, active learning strategies will be developed to satisfy such informativity conditions in an efficient and effective manner.