Multiple Faults Estimation in Dynamical Systems: Tractable Design and Performance Bounds

TL;DR

This paper introduces a tractable nonlinear fault isolation filter for dynamical systems with additive and multiplicative faults, providing explicit performance bounds and demonstrating effectiveness in automated vehicle safety systems.

Contribution

It presents a novel filter architecture combining control and machine learning tools, with explicit operator and performance bounds for simultaneous fault estimation.

Findings

Estimation error converges exponentially to zero for constant faults.

Performance bounds closely match actual estimation errors.

Validated on SAE level 4 vehicle safety systems.

Abstract

In this article, we propose a tractable nonlinear fault isolation filter along with explicit performance bounds for a class of nonlinear dynamical systems. We consider the presence of additive and multiplicative faults, occurring simultaneously and through an identical dynamical relationship, which represents a relevant case in several application domains. The proposed filter architecture combines tools from model-based approaches in the control literature and regression techniques from machine learning. To this end, we view the regression operator through a system-theoretic perspective to develop operator bounds that are then utilized to derive performance bounds for the proposed estimation filter. In the case of constant, simultaneously and identically acting additive and multiplicative faults, it can be shown that the estimation error converges to zero with an exponential rate. The performance of the proposed estimation filter in the presence of incipient faults is validated through an application on the lateral safety systems of SAE level 4 automated vehicles. The numerical results show that the theoretical bounds of this study are indeed close to the actual estimation error.