On Approximate Diagnosability of Nonlinear Systems

TL;DR

This paper introduces a new concept called approximate diagnosability for nonlinear systems, enabling detection of faults within finite delay and accuracy despite measurement errors, using symbolic models and formal methods.

Contribution

It proposes a novel framework for approximate diagnosability of nonlinear systems with unknown inputs and quantized outputs, utilizing symbolic models for analysis.

Findings

Derived symbolic models approximating nonlinear systems within desired accuracy

Established relation between symbolic model diagnosability and original system

Provided a method to verify approximate diagnosability using formal tools

Abstract

This paper deals with diagnosability of discrete-time nonlinear systems with unknown inputs and quantized outputs. We propose a novel notion of diagnosability that we term approximate diagnosability, corresponding to the possibility of detecting within a finite delay and within a given accuracy if a set of faulty states is reached or not. Addressing diagnosability in an approximate sense is primarily motivated by the fact that system outputs in concrete applications are measured by sensors that introduce measurement errors. Consequently, it is not possible to detect exactly if the state of the system has reached or not the set of faulty states. In order to check approximate diagnosability on the class of nonlinear systems we use tools from formal methods. We first derive a symbolic model approximating the original system within any desired accuracy. This step allows us to check approximate diagnosability of the symbolic model. We then establish the relation between approximate diagnosability of the symbolic model and of the original nonlinear system.