Abstract:We present a physics-informed framework for system identification based on randomized stable atomic features. Impulse responses are represented as random superpositions of stable atoms, namely damped complex exponentials associated with poles sampled inside a prescribed disk. Identification is then cast as a convex regularized least-squares problem with optional linear, second-order-cone, and KYP constraints. The approach generalizes random Fourier and random Laplace features to the damped, nonstationary regime relevant to engineering systems while retaining modal interpretability and scalable finite-dimensional computation. The main analytic point is an operator-theoretic Disk-Bochner viewpoint: positive measures over stable poles generate positive-definite kernels with a radius-dependent shift defect, while a converse scalar disk moment representation for an arbitrary kernel is characterized by subnormality of the canonical shift. We prove this statement, establish an RKHS-to-l1 embedding, show that sampled poles induce a valid finite atomic gauge, discuss random-feature convergence, and state sparse-recovery guarantees conditionally on the restricted-eigenvalue properties of the realized disk-Vandermonde or input-output design matrix. We also connect the normalized transfer function problem to Nevanlinna-Pick interpolation and LFT set-membership. The framework directly encodes stability margins, modal localization, DC-gain bounds, monotonicity, passivity, relative degree, settling-time targets, and time/frequency-domain error bounds. Numerical comparisons illustrate how physically meaningful priors can compensate for poor excitation and improve constrained impulse-response recovery in an under-informative data setting.
| Comments: | Extended version of the conference paper submitted for IFAC World Congress, 2026 |
| Subjects: | Systems and Control (eess.SY); Machine Learning (cs.LG) |
| MSC classes: | 93E10 |
| ACM classes: | I.6.5 |
| Cite as: | arXiv:2605.14351 [eess.SY] |
| (or arXiv:2605.14351v1 [eess.SY] for this version) | |
| https://doi.org/10.48550/arXiv.2605.14351 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Rajiv Singh [view email]
[v1]
Thu, 14 May 2026 04:25:07 UTC (952 KB)