Adaptive Exponential Fault Estimation for 1-D Linear Parabolic PDEs With Process Uncertainties

The problem of fault estimation is addressed for one-dimensional (1-D) linear boundary control and boundary observation (BCBO) parabolic partial differential equations (PDEs) with a faulty boundary measurement. The considered plant is subjected to simultaneous unknown multiplicative faults entering the boundary input and boundary measurement. Difficulties arise due to the coupling between the sensor fault parameter and unknown boundary state appearing in the measurement. With the only boundary input and faulty boundary measurement, it is rather challenging to estimate the accurate values of faults and state simultaneously. Therefore, most existing results only consider correct and healthy measurement for PDE systems. To this end, novel adaptation laws and an adaptive observer are designed in this work to provide exponential convergent joint fault-state estimation, where we design and leverage a set of novel filters. It is first time that unknown multiplicative fault parameter in the measurement can be estimated accurately in the PDE systems.

Automated summary

In this paper, a solution for fault estimation is proposed for one-dimensional linear boundary control and boundary observation parabolic PDEs, which can accurately estimate the unknown multiplicative fault parameter in the measurement.