Perron-Frobenius Contractive Operator Matching for Data-Driven Reachable Fault Identification and Recovery
New framework learns from data to detect actuator failures in complex systems like spacecraft with certifiable bounds.
A team from Caltech and NASA's Jet Propulsion Laboratory has published a novel AI framework for making complex systems like spacecraft more resilient to failures. The method, called Perron-Frobenius Contractive Operator Matching, shifts the problem from tracking individual trajectories to predicting the evolution of entire state probability densities. By constructing a library of fault-indexed Perron-Frobenius (PF) operators, the system can model how a system's behavior distribution changes under different actuator fault scenarios. This provides a unified, data-driven approach to Fault Detection, Identification, and Recovery (FDIR).
The core innovation is using the mathematical link between stochastic dynamics and deterministic PF operators via the Fokker-Planck equation. This allows the team to define forward reachable density families and establish rigorous, certifiable bounds on the divergence between faulty and nominal operations using the 2-Wasserstein metric. These bounds provide quantitative conditions for when a fault is detectable and identifiable. The fault-indexed operators are not pre-programmed but are learned directly from trajectory data using a technique called Flow Map Matching (FMM).
For practical deployment, the framework co-trains a contraction certificate alongside the operators. This certificate bounds the approximation error between the learned model and the real system's behavior. During online operation, the system performs continuous fault parameter fitting over a continuous parameter space, allowing it to generalize to out-of-distribution (OOD) fault scenarios not seen in training. Once a fault is identified, recovery is executed using reachable density propagation and Gaussian mixture covariance steering to guide the system back to a safe operating state. The method was successfully validated on a high-fidelity, 10-state model of a spacecraft attitude-control system with four reaction wheels, a critical application where actuator failures can be catastrophic.
- Uses Perron-Frobenius operators to model state probability densities, not just trajectories, for a more robust fault analysis.
- Establishes certifiable 2-Wasserstein bounds for fault detectability/identifiability and learns operators from data via Flow Map Matching.
- Validated on a 10-state spacecraft model, enabling continuous online fault parameter fitting and recovery control via covariance steering.
Why It Matters
Enables more autonomous, resilient spacecraft and industrial systems that can self-diagnose and recover from unforeseen actuator failures.