Mittag-Leffler stabilization for coupled fractional reaction-diffusion neural networks subject to boundary matched disturbance

In this paper, we study the boundary stabilization for a class of neural networks with non-identical nodes described by the fractional Orr-Sommerfeld (OS) equation cascaded with the fractional Squire equation and fractional ordinary differential equations (ODEs), in which the disturbances flow to the control end of both the OS equation and the Squire equation. By applying the Backstepping transform, the diffusion subsystems in the considered neural networks are decoupled, while only the ODEs are still cascaded with the diffusion terms through the Neumann interconnection. By the active disturbance rejection control (ADRC) approach, two auxiliary systems are constructed to compensate each disturbance by an estimator without high gain. Finally, a boundary feedback control law is designed to achieve the Mittag-Leffler stability of the neural networks in the closed-loop.