This paper presents a new model-based fault resilient control scheme for a class of nonlinear distributed parameter systems (DPS) represented by parabolic partial differential equations (PDE) in the presence of actuator faults. A Luenberger-like observer on the basis of nonlinear PDE representation of DPS is developed with boundary measurements. A detection residual is generated by taking the difference between the measured output of the DPS and the estimated one given by the observer. Once a fault is detected, an unknown actuator fault parameter vector together with a known basis function is utilized to adaptively estimate the fault dynamics. A novel tuning algorithm is derived to estimate the unknown actuator fault parameter vector. Next, in order to achieve resilience, the controller from the healthy scenario is adjusted to mitigate the faults by using both estimated fault dynamics and a secondary measurement. Subsequently, an explicit formula is developed to estimate the time-to-resilience (TTR). Finally, a nonlinear example is utilized to illustrate the effectiveness of the proposed scheme.


Electrical and Computer Engineering

Second Department

Computer Science

Publication Status

Open Access

Keywords and Phrases

adaptive estimation; distributed parameter systems; Fault detection; resilient control

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2024 The Authors, All rights reserved.

Publication Date

01 Jan 2024