Low Dimensional Anti-Disturbance Fuzzy Control for 2-D Spatial Parabolic PDE Systems with Nonlinear ODE Exosystem via Fuzzy Disturbance Observer

A design method of low dimensional anti-disturbance fuzzy control via fuzzy disturbance observer (FDO) is proposed for a class of 2-dimensional (2-D) spatial nonlinear parabolic partial differential equation (PDE) systems with multiple time-domain disturbances including the disturbance modeled by the nonlinear ordinary differential equation (ODE) exosystem. First, the modal decomposition technique is applied to the PDE system to derive a low dimensional slow subsystem, which is subsequently approximated by a T-S fuzzy model. Next, a radial basis function (RBF) fuzzy system is employed and then an FDO is developed to estimate the modeled disturbance. Based on T-S fuzzy model and FDO, a low dimensional anti-disturbance fuzzy control method is developed to satisfy the uniformly ultimately boundedness (UUB). Finally, the effectiveness of the proposed design method is demonstrated on the control of a diffusion-reaction system.