Data-Driven Stable Neural Feedback Loop Design

This paper proposes a data-driven approach to design a feedforward Neural Network (NN) controller with a stability guarantee for plants with unknown dynamics. We first introduce data-driven representations of stability conditions for Neural Feedback Loops (NFLs) with linear plants, which can be formulated into a semidefinite program (SDP). Subsequently, this SDP constraint is integrated into the NN training process to ensure stability of the feedback loop. The whole NN controller design problem can be solved by an iterative algorithm. Finally, we illustrate the effectiveness of the proposed method compared to model-based methods via numerical examples.