Robust Fault Diagnosis of Uncertain One-dimensional Wave Equations

Satadru Dey, Scott J. Moura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


Unlike its Ordinary Differential Equation (ODE) counterpart, fault diagnosis of Partial Differential Equations (PDE) has received limited attention in existing literature. The main difficulty in PDE fault diagnosis arises from the spatio-temporal evolution of the faults, as opposed to temporal-only fault dynamics in ODE systems. In this work, we develop a fault diagnosis scheme for one-dimensional wave equations. A key aspect of this fault diagnosis scheme is to distinguish the effect of uncertainties from faults. The scheme consists of a PDE observer whose output error is treated as a fault indicating residual signal. Furthermore, a threshold on the residual signal is utilized to infer fault occurrence. The convergence properties of the PDE observer and residual signal are analyzed via Lyapunov stability theory. The threshold is designed based on the uncertain residual dynamics and the upper bound of the uncertainties. Simulation studies are performed to illustrate the effectiveness of the proposed fault diagnosis scheme.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538613955
StatePublished - Jul 2 2018
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference57th IEEE Conference on Decision and Control, CDC 2018
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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