Model order reduction of deep structured state-space models: A system-theoretic approach
This work addresses the need for parsimonious and efficient models in control design applications, representing an incremental improvement by applying existing regularization techniques to a specific bottleneck in SSMs.
The paper tackles the problem of excessively large model orders in deep structured state-space models (SSMs) for control design by introducing system-theoretic model order reduction techniques, specifically modal ℓ₁ and Hankel nuclear norm regularization, which reduce model complexity while maintaining accuracy, as demonstrated on real-world aircraft ground vibration data.
With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. 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 often suffer from excessively large model orders, which render them unsuitable for control design purposes. The current paper addresses this challenge by means of system-theoretic model order reduction techniques that target the linear dynamical blocks of SSMs. We introduce two regularization terms which can be incorporated into the training loss for improved model order reduction. In particular, we consider modal $\ell_1$ and Hankel nuclear norm regularization to promote sparsity, allowing one to retain only the relevant states without sacrificing accuracy. The presented regularizers lead to advantages in terms of parsimonious representations and faster inference resulting from the reduced order models. The effectiveness of the proposed methodology is demonstrated using real-world ground vibration data from an aircraft.