Output-Feedback Adaptive Fault-Tolerant Boundary Control for Parabolic PDE Systems.

This letter investigates the output-feedback fault-tolerant boundary control problem for a class of parabolic PDE systems subject to both biased harmonic disturbances and multiplicative actuator faults. In this problem, a trajectory tracking objective is given and only the boundary measurement is available. To achieve state estimation, some filters are introduced, and the observer is expressed as a liner combination of these filters. To deal with disturbances and actuator faults, the adaptive parameter updating laws are designed via gradient-descent method to estimate the uncertain coefficients. To achieve trajectory tracking, a reference variable is introduced and an error system is constructed based on which the backstepping tracking control law is designed. It is proved that the proposed backstepping control law can achieve the trajectory tracking objective. Finally, the efficiency of our method is confirmed by simulation studies.