Data-to-Certificates (D2C): Koopman Supereigenfunctions for Stability, Safety, and Control
Abstract
Traditional dynamical system models, including Koopman operator representations, are fundamentally equality-based, whereas many analysis and control tools rely on inequalities. This mismatch motivates representations that are intrinsically aligned with certification tasks involved in the analysis and control synthesis problems. In this paper, we propose a \emph{data-to-certificates (D2C)} paradigm that bypasses explicit model construction and directly learns certificates from data. We introduce \emph{supereigenfunctions} of the Koopman operator as an inequality-based generalization of eigenfunctions that define exponential growth envelopes encoding stability, safety, and uncertainty propagation, thereby serving as certificates for a range of control objectives. We establish their theoretical foundations and show that the associated rates recover intrinsic dynamical quantities such as Lyapunov exponents. Two complementary constructions are developed: a geometric approach based on the multiplicative ergodic theorem (MET), and a resolvent/Gramian formulation that enables computation directly from trajectory data. The resulting framework yields certificates that can be used for stability and contraction analysis, as well as stabilizing and safety-critical control synthesis via convex quadratic programming-based optimization program. Numerical examples demonstrate the effectiveness of the proposed data-driven certification approach for stabilization, contraction, and safe control design.
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BibTeX
@misc{vaidya2026datatocertificates,
title = {{Data-to-Certificates (D2C): Koopman Supereigenfunctions for Stability, Safety, and Control}},
author = {Umesh Vaidya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00178},
eprint = {2610.00178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00178},
}
RIS
TY - UNPB
TI - Data-to-Certificates (D2C): Koopman Supereigenfunctions for Stability, Safety, and Control
AU - Umesh Vaidya
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00178
UR - https://arxiv.org/abs/2610.00178
AB - Traditional dynamical system models, including Koopman operator representations, are fundamentally equality-based, whereas many analysis and control tools rely on inequalities. This mismatch motivates representations that are intrinsically aligned with certification tasks involved in the analysis and control synthesis problems. In this paper, we propose a \emph{data-to-certificates (D2C)} paradigm that bypasses explicit model construction and directly learns certificates from data. We introduce \emph{supereigenfunctions} of the Koopman operator as an inequality-based generalization of eigenfunctions that define exponential growth envelopes encoding stability, safety, and uncertainty propagation, thereby serving as certificates for a range of control objectives. We establish their theoretical foundations and show that the associated rates recover intrinsic dynamical quantities such as Lyapunov exponents. Two complementary constructions are developed: a geometric approach based on the multiplicative ergodic theorem (MET), and a resolvent/Gramian formulation that enables computation directly from trajectory data. The resulting framework yields certificates that can be used for stability and contraction analysis, as well as stabilizing and safety-critical control synthesis via convex quadratic programming-based optimization program. Numerical examples demonstrate the effectiveness of the proposed data-driven certification approach for stabilization, contraction, and safe control design.
ER -