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Dey, S., Perez, H.E. and Moura, S.J. (2019) Robust Fault Detection of a Class of Uncertain Linear Parabolic PDEs. Automatica, 107, 502-510.
https://doi.org/10.1016/j.automatica.2019.06.014

has been cited by the following article:

• TITLE: Backstepping-Based Distributed Abnormality Detection for Nolinear Parabolic Distributed Prameter Systems

  AUTHORS: Lei Chen

  KEYWORDS: Abnormality Detection, Backstepping, Nonlinear Parabolic Systems, Distributed Parameter Systems, Lyapunov Function

  JOURNAL NAME: Engineering, Vol.14 No.7, July 28, 2022

  ABSTRACT: In this paper, we proposed a model-based abnormality detection scheme for a class of nonlinear parabolic distributed parameter systems (DPSs). The proposed methodology consists of the design of an observer and an abnormality detection filter (ADF) based on the backstepping technique and a limited number of in-domain measurements plus one boundary measurement. By taking the difference between the measured and estimated outputs from observer, a residual signal is generated for fault detection. For the detection purpose, the residual is evaluated in a lumped manner and we propose an explicit expression for the time-varying threshold. The convergence properties of the PDE observer and the residual are analyzed by Lyapunov stability theory. Eventually, the proposed abnormality detection scheme is demonstrated on a nonlinear DPS.