Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control matched disturbance

This paper addresses the Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control subject to the control matched disturbance. The active disturbance rejection control (ADRC) approach is adopted for developing the control law. A state‐feedback scheme is designed to estimate the disturbance by constructing two auxiliary systems: One is to separate the disturbance from the original system to a Mittag‐Leffler stable system and the other is to estimate the disturbance finally. The proposed control law compensates the disturbance using its estimation and stabilizes system asymptotically. The closed‐loop system is shown to be Mittag‐Leffler stable and the constructed auxiliary systems in the closed loop are proved to be bounded. This is the first time for ADRC to be applied to a system described by the fractional partial differential system without using the high gain.