Disturbance Observer-Based Hysteretic Quantized Fuzzy Control for Nonlinear Parabolic PDE System

This paper investigates the disturbance observer-based hysteretic quantized fuzzy control for nonlinear parabolic partial differential equation (PDE) system with disturbances. The system contains two types of disturbances, one is bounded disturbance from outside, and the other is generated along with the control input and can be depicted by the ordinary differential equation (ODE). We initially adopt the Galerkin technique to separate the PDE system into fast subsystem and slow subsystem, and the slow subsystem can describe the main dynamics properties of the system. Then, we obtain a fuzzy system by the Takagi-Sugeno fuzzy technique. Next, we design the disturbance observer based on the external ODE system. On this basis, a hysteresis quantized controller is designed to be semi-globally uniformly ultimately bounded. Finally, a simulation example shows the effectiveness.