The construction of generalized mathematical models is proposed that describe the dynamics of a controlled belt conveyor with a variable angle between the horizontal plane and the plane of the belt. The models under consideration are defined using nonlinear nonstationary systems of four differential equations with switching. Switching modes are characterized by a change in the loading and unloading sequence. Statements of optimal control problems are presented under restrictions on the magnitude of control and on the speed of control. Synthesis of neural network controllers for stabilization of the angular position of the conveyor is carried out. Controllers are synthesized using such direct propagation neural networks for which reinforcement learning is implemented based on the optimization algorithm of differential evolution. A comparative analysis of the effectiveness of synthesized controllers is carried out. Algorithmic support for modeling controlled conveyor systems is developed using intelligent analysis and global parametric optimization methods. The results of computational experiments are presented. The obtained results can find application in solving problems of optimal stabilization of dynamic systems with switching.