Geometric Fault Identification via Mirror Descent Learning

TL;DR

This paper introduces a geometric fault detection and identification method for nonlinear systems using a hybrid observer with neural networks and mirror descent adaptation, demonstrated on spacecraft control.

Contribution

It develops a novel geometric approach combined with mirror descent laws for fault isolability and neural network adaptation in nonlinear control systems.

Findings

Fault detection accuracy improved with geometric analysis.

Mirror descent laws enhance neural network fault estimation.

Method validated on spacecraft attitude control system.

Abstract

This paper develops a fault detection and identification (FDI) method for nonlinear control-affine systems under simultaneous actuator and sensor faults. We adopt a geometric approach to study the isolability of faults in the sense of the principal angles between subspaces corresponding to each actuator and sensor fault. As for the fault identification, a hybrid estimator that consists of a Luenberger-like observer with contraction guarantees is developed. Moreover, neural networks are embedded in the mentioned observer to estimate actuator and sensor faults. Considering that the training dataset for neural networks cannot be representative of every fault scenario, the last layer of each network is adapted using mirror descent-based laws. The mirror descent-based adaptive laws impose isolability conditions for fault channels and do not assume a quadratic parameter estimation space to consider the geometry of the fault subspaces. A Lyapunov-based analysis establishes that the state and parameter estimation errors are uniformly ultimately bounded. The effectiveness of our proposed FDI method is illustrated on the 3-axis attitude control system of a spacecraft.