Crane systems have been widely applied in logistics due to their efficiency of transportation. The parameters of a crane system may vary from each transport, therefore the anti-sway controller should be designed to be insensitive to the variation of system parameters. In this paper, we focus on pure neural network adaptive tracking controller design issue that does not require the parameters of crane systems, i.e. the trolley mass, the payload mass, the cable lengths, and etc. The proposed neural network controller only requires the output feedback signals of the trolley, i.e. the position and the velocity, which means no sway measuring equipment is needed. The Lyapunov method is utilized to design the weights update law of neural network, and the robustness of the proposed controller is proved by the Lyapunov stability theory. The results of numerical simulations show that the proposed neural network controller has excellent performance of trolley position tracking and payload anti-sway controlling. KEYWORDS adaptive control, anti-sway control, double-pendulum crane systems, Lyapunov stability theory, neural network control 1 | INTRODUCTION Crane systems with cable hoisting mechanism are typically under-actuated systems. They play an important role in logistics and are widely used in container harbors, railway container yards, and other industrial factories. As cable hoisting mechanism is adopted, the weight of the crane is reduced, but the payload swings unavoidably during the transportation as well as reaching the desired position. The sway of the payload decreases the efficiency of crane's transportation and may result in hazards, such as collision, tip over, and etc. To improve the effectiveness and the safety of crane, researchers proposed many anti-sway control strategies to position the trolley accurately and eliminate the payload sway. All the anti-sway control strategies aim to: i) move the trolley safely, fast, and accurately to the desired position, and ii) decrease the sway of the payload as much as possible during the transportation and eliminate the residual sway when reaching the desired position. TIf the parameters of crane systems are exactly known, open-loop control strategies can work effectively. Singhose et al. reviewed the command shaping/input shaping [1] and implemented the method on doublependulum crane systems [2,3]. It shows that the method