Despite the fact that the hydrodynamic lubrication is a self-controlled process, we designed control systems based on proportional integral (PI) controller, adaptive PI controller, and Deep Q network (DQN)-agent to minimize the friction torque in a conical fluid-film bearing. The bearing construction allows the shaft axial displacement and, as the result, the regulation of the bearing average clearance due to the controlled supply pressure. The main challenge is that the friction torque minimization may lead to the loss of load-carrying capacity and the contact in the shaft-bearing tribocouple. The other challenge is that random events may have an influence on the hydrodynamic lubrication parameters, therefore, changing the load-carrying capacity and the friction torque. So, the proposed control systems were designed and tested under the conditions of limited lateral shaft displacements and the action of a random external force. The tests were performed using simulation models of a controlled rotating machine in matlab software. The rotating machine simulation model includes modules of the rigid shaft, the coupling with linear axial reaction, and the conical bearing. The bearing module is based on the numerical solution of the generalized Reynolds equation and its nonlinear approximation with fully connected neural networks. The obtained results demonstrated that the application of an adaptive PI controller or a DQN agent allows decreasing friction torque in a bearing under the conditions of a random external force. The goal of a DQN agent is self-learning in contrast to an adaptive PI controller that needs to be tuned.