Observer-Based Boundary Fuzzy Control Design of Nonlinear Parabolic PDE Systems Using Mobile Sensors

This article studies the boundary fuzzy control problem for nonlinear parabolic partial differential equation (PDE) systems under spatially noncollocated mobile sensors. In a real setup, sensors and actuators can never be placed at the same location, and the noncollocated setting may be beneficial in some application scenarios. The control design is very difficult due to the noncollocated mobile observation, which can be solved by an observer-based technique. At first, a Takagi–Sugeno fuzzy PDE model is devoted to accurately representing the nonlinear parabolic PDE system. Next, we present a state estimation scheme including fuzzy Luenberger-type PDE state observer plus mobile sensor guidance. Then, an observer-based boundary fuzzy controller is posed to render the resulting closed-loop system exponentially stable, and the exponential decay rate is increased by the designed mobile sensor guidance laws. At last, two examples verify the proposed method.