Perron-Frobenius Contractive Operator Matching for Data-Driven Reachable Fault Identification and Recovery
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915941679366144 |
|---|---|
| author | Ibrahim, Joshua D. Taheri, Mahdi Chung, Soon-Jo Hadaegh, Fred Y. |
| author_facet | Ibrahim, Joshua D. Taheri, Mahdi Chung, Soon-Jo Hadaegh, Fred Y. |
| contents | This paper focuses on data-driven fault detection, identification, and recovery (FDIR) for nonlinear control-affine systems under actuator faults. We create a unified framework in the space of probability densities, rather than on individual trajectories, using fault-indexed Perron--Frobenius (PF) operators to predict the evolution of state distributions under different fault profiles. By leveraging the probability-flow representation of the Fokker--Planck equation, we construct deterministic PF operators that reproduce exact stochastic marginals, define forward reachable density families, and establish certifiable 2-Wasserstein bounds on the divergence between fault-driven and nominal density evolutions. These provide quantitative conditions for the detectability and identifiability of various faults. The fault-indexed operators are learned from trajectory data via flow map matching (FMM), and we demonstrate that the observable FMM residual directly bounds the approximation error of the operator in the 2-Wasserstein metric. Additionally, we co-train a contraction certificate that bounds the gap between the learned operator family, the actual fault-driven density flow, and the nominal dynamics. The operator library is then used online for continuous fault parameter fitting over a continuous parameter space to generalize the learned operators to out-of-distribution (OOD) scenarios. To carry out the recovery control, we employ reachable density propagation and Gaussian mixture covariance steering. The proposed framework is validated on a 10-state spacecraft attitude-control system with four reaction wheels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perron-Frobenius Contractive Operator Matching for Data-Driven Reachable Fault Identification and Recovery Ibrahim, Joshua D. Taheri, Mahdi Chung, Soon-Jo Hadaegh, Fred Y. Systems and Control Signal Processing This paper focuses on data-driven fault detection, identification, and recovery (FDIR) for nonlinear control-affine systems under actuator faults. We create a unified framework in the space of probability densities, rather than on individual trajectories, using fault-indexed Perron--Frobenius (PF) operators to predict the evolution of state distributions under different fault profiles. By leveraging the probability-flow representation of the Fokker--Planck equation, we construct deterministic PF operators that reproduce exact stochastic marginals, define forward reachable density families, and establish certifiable 2-Wasserstein bounds on the divergence between fault-driven and nominal density evolutions. These provide quantitative conditions for the detectability and identifiability of various faults. The fault-indexed operators are learned from trajectory data via flow map matching (FMM), and we demonstrate that the observable FMM residual directly bounds the approximation error of the operator in the 2-Wasserstein metric. Additionally, we co-train a contraction certificate that bounds the gap between the learned operator family, the actual fault-driven density flow, and the nominal dynamics. The operator library is then used online for continuous fault parameter fitting over a continuous parameter space to generalize the learned operators to out-of-distribution (OOD) scenarios. To carry out the recovery control, we employ reachable density propagation and Gaussian mixture covariance steering. The proposed framework is validated on a 10-state spacecraft attitude-control system with four reaction wheels. |
| title | Perron-Frobenius Contractive Operator Matching for Data-Driven Reachable Fault Identification and Recovery |
| topic | Systems and Control Signal Processing |
| url | https://arxiv.org/abs/2604.15470 |