Randomized Atomic Feature Models for Physics-Informed Identification of Dynamic Systems
This work addresses the challenge of identifying dynamic systems under insufficient excitation, where achieving physical consistency, stability, and interpretability simultaneously remains difficult. To this end, we propose a physics-informed framework based on stochastic stable atomic features. The impulse response is modeled as a random superposition of damped complex exponential atoms, and physically interpretable modal parameters are efficiently recovered through convex regularized least squares subject to explicit stability constraints. By integrating perspectives from Disk–Bochner operators, reproducing kernel Hilbert space (RKHS) theory, and the Kalman–Yakubovich–Popov (KYP) lemma, the method embeds engineering priors—such as stability and DC gain—into a finite-dimensional optimization framework. Experimental results demonstrate that the proposed approach significantly improves identification accuracy under poorly excited conditions while rigorously preserving system stability and structural interpretability.