On generating training data for provably stable neural network-based control

In the recent work (Li et al., 2024), a neural network-based control framework with provable stability guarantees was proposed for nonlinear systems. While effective, a key practical challenge in deploying this framework lies in solving the optimization problems required for generating training data. This short communication complements (Li et al., 2024) by presenting a block-alternating iterative procedure for addressing these optimization problems. Basic theoretical properties of the proposed algorithm, including feasibility preservation and convergence to stationary points, are established. The effectiveness of the approach is illustrated through a temperature regulation experiment.