Preventing chattering phenomenon in load following control of the Pressurized Water Reactor (PWR) is still a main challenge. This article focuses on the chattering-free and rapid load following control strategy for PWR. Firstly, by proposing a newly adaptive updated law, the Radial Basis Function Neural Networks (RBFNNs) is employed to compensate the unmeasured states of relative delayed neutron precursor density, average fuel temperature and uncertain disturbances simultaneously online. On this basis, a fixed-time stable controller including saturation function is constructed to guarantee tha...