Model Order Reduction of Deep Structured State-Space Models: A System-Theoretic Approach

With a specific emphasis on control design objectives, achieving accuratesystem modeling with limited complexity is crucial in parametric systemidentification. The recently introduced deep structured state-space models(SSM), which feature linear dynamical blocks as key constituent components,offer high predictive performance. However, the learned representations oftensuffer from excessively large model orders, which render them unsuitable forcontrol design purposes. The current paper addresses this challenge by means ofsystem-theoretic model order reduction techniques that target the lineardynamical blocks of SSMs. We introduce two regularization terms which can beincorporated into the training loss for improved model order reduction. Inparticular, we consider modal ℓ_1 and Hankel nuclear norm regularizationto promote sparsity, allowing one to retain only the relevant states withoutsacrificing accuracy. The presented regularizers lead to advantages in terms ofparsimonious representations and faster inference resulting from the reducedorder models. The effectiveness of the proposed methodology is demonstratedusing real-world ground vibration data from an aircraft.