Output feedback stabilization of multi-dimensional Kirchhoff equation with general corrupted boundary observation by active disturbance rejection control

In this paper, the boundary output feedback stabilization of a multi-dimensional Kirchhoff plate equation with boundary control is considered. The boundary measurement is suffered from external disturbance that depends both on time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted for the first time on the corrupted output feedback stabilization for systems described by multi-dimensional partial differential equations (PDEs). An output feedback disturbance estimator is designed to estimate the disturbance, based on an infinite number of ordinary differential equations obtained from the original multi-dimensional system by infinitely many time dependent test functions. The disturbance is canceled in the disturbance estimator based feedback loop. All subsystems in the closed-loop are shown to be asymptotically stable. In particular, the system with constant disturbance in observation is shown to be exponentially stable with rejecting the disturbance in finite time. The numerical simulations are presented for illustration.