Safe, Real-Time Active Model Discrimination and Fault Diagnosis for Nonlinear Systems via Differentiable Reachability

2026-06-17

AI Summary

This work proposes an active fault diagnosis and model identification method for continuous-time nonlinear systems subject to process and measurement disturbances, balancing safety and real-time performance. By formulating a time-varying output-feedback optimization strategy over a finite horizon, the approach simultaneously enforces state-input safety constraints and generates excitation signals capable of uniquely distinguishing among candidate models. The key innovation lies in the first-time integration of differentiable reachability analysis with interval over-approximation techniques, enabling the design of a differentiable objective function that minimizes the overlap between output reachable sets of distinct models to achieve deterministic diagnosis. Leveraging a JAX-based gradient optimization framework, the method supports efficient online computation. Validation on high-dimensional systems—including quadrotors, fighter jets, differential-drive robots, and quadrupeds—demonstrates its ability to handle up to 11 fault classes with diagnosis latency under 50 ms, outperforming existing approaches in both success rate and speed while providing formal safety guarantees.

Abstract

We present a safe, real-time algorithm for active fault diagnosis and model discrimination for uncertain continuous-time nonlinear systems with process and measurement disturbances. Given a finite set of candidate models representing nominal and faulty modes, including actuator and sensor faults, we formulate an output-feedback, time-varying policy optimization problem that (i) robustly enforces state-input safety constraints over a finite horizon and (ii) drives the system to produce sampled measurements consistent with at most one model, enabling deterministic diagnosis. To solve this problem in real time, we develop a tractable approximation using interval over-approximations of reachable state and output sets, and encode diagnosability via a differentiable objective that penalizes overlap between the reachable output sets of possible models. The resulting optimization is solved efficiently online with gradient-based methods using JAX and differentiable reachability primitives. We evaluate our method on sensor and actuator fault diagnosis (up to 11 fault modes) in several high-dimensional nonlinear robotic systems, including a simulated quadrotor and fighter-jet model, a hardware differential-drive robot, and quadrupedal navigation. Across these case studies, our approach achieves reliable model discrimination in under 50 ms, outperforming baselines in discrimination success rate and speed while providing formal safety guarantees.

Problem

• active fault diagnosis
• model discrimination
• nonlinear systems
• safety constraints
• real-time

Innovation

• differentiable reachability
• active fault diagnosis
• model discrimination
• safety-critical control
• real-time optimization