Adaptive Exponential Fault Estimation for 1-D Linear Parabolic PDEs With Process Uncertainties
针对边界测量存在故障的一维线性抛物型偏微分方程系统，设计了自适应观测器，首次实现了对测量中未知乘性故障参数的精确指数收敛估计。
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.