Disturbance observer-based H∞ quantized fuzzy control of nonlinear delayed parabolic PDE systems

This research presents a novel quantized fuzzy control technique based on Luenberger-like disturbance observer for a class of nonlinear delayed parabolic partial differential equation (PDE) systems, which are influenced by two distinct types of disturbances. To begin with, the PDE system is decomposed using the Galerkin approach, resulting in a finite-dimensional slow ordinary differential equation (ODE) subsystem and an infinite-dimensional fast ODE subsystem. Then, the slow system which effectively characterizes the active mechanical behavior of the initial model is fuzzified by the Takagi–Sugeno fuzzy technique to obtain a relatively accurate model. Subsequently, based on disturbance observer, three types of quantized fuzzy controllers are devised to ensure that the system become semi-globally uniformly ultimately bounded. Furthermore, the $H_{\infty }$ performance control problem with different quantizers is investigated in this study. Lastly, the numerical simulation demonstrates the effectiveness of the three quantizers.