The straightness control of a fully mechanized working face is the key technology used in intelligent coal mining, so the position control of a hydraulic support multi-cylinder moving system is of great significance. However, due to the harsh environment of coal mines, complex friction, external disturbances, and the coupling relationship between adjacent cylinders, the accuracy of position control is restricted. Therefore, an output cooperative controller is proposed in this paper for a multi-cylinder system. A high-order sliding mode observer is utilized to estimate the system states with the only available output position signal. A neural network disturbance observer is applied to estimate the lump disturbance of the strict-feedback model, including the system uncertainty, disturbance force and the coupling force between adjacent cylinders. Then, continuous motion position tracking simulation is conducted and the estimation performance of the state observer and neural network is analyzed. Furthermore, a multi-cylinder collaborative control test rig is designed, and experiments based on the actual actions of the hydraulic support are conducted. The results show that the proposed output cooperative controller has an excellent position control performance compared with the traditional proportional–integral controller.