## 1 Introduction  
Pneumatic actuators have been widely used in industrial applications due to the advantages of having a high power/mass ratio, being low cost, clean, and easily serviced [1; 2; 3]. Some examples are pneumatic force actuator systems [1; 4], positioning control systems [5], and rehabilitation devices [6]. However, the dynamics of the pneumatic system are complicated, including the nonlinearities of pressure dynamics, the compressibility of air, unmodeled friction, and random disturbances, etc. The unmodeled dynamics, disturbances, and inaccurate mathematic models result in achieving precise motion control of pneumatic cylinders being a challenging task. The linear control strategy and modified linear control techniques [5; 7; 8] are widely applied to the pneumatic systems, but the strong nonlinear dynamics of pneumatic systems restrict the capability of a linear controller in achieving a high precision tracking performance. Therefore, the model-based control strategy is considered for pneumatic systems [9]. The sliding mode control [10; 11; 12] method is introduced to pneumatic systems for strong robustness; however, it has limited capacity to compensate for nonlinear dynamics. In addition, the backstepping [13] technique is used for controller design and stability analysis of the pneumatic systems. The adaptive control strategy [14] is used for pneumatic systems to obtain a more precise model compensation but is vulnerable to disturbances. Adaptive robust control (ARC) [15; 16] takes advantages of robust control and adaptive control to acquire robustness and better tracking performance. [PERSON] et al. [17; 18] devised the adaptive robust controller for a parallel manipulator driven by pneumatic muscles, and significant performance was achieved. The ARC scheme also serves to design a controller for position tracking of the pneumatic cylinder [19]. Although the performance of ARC controller for pneumatic systems is improved compared with other nonlinear controllers, several problems exist. First, the ARC improves the model compensation by the accurate estimation of unknown parameters which needs a known structure for the system dynamics. However, the unmodeled dynamics of complex pneumatic motion progress is hard to describe as a known structure due to the lack of knowledge concerning physical phenomena, including friction force, heat transfer, random disturbances, etc. Moreover, too complicated mathematical models are not convenient for controller design. Second, the existing ARC controllers for pneumatic systems are requested for known bounds for all unknown parameters and these are not easy to acquire. Furthermore, too large a range for bounds of unknown parameters will lead to a saturation problem [20]. Fortunately, neural networks (NN) have been used in controller design for their excellent ability to approximate arbitrary unknown nonlinearities [21], including the unmodeled dynamics and random disturbances. Therefore, NN controllers have been designed for high nonlinear pneumatic systems to obtain better model compensation [22; 23; 24; 25]. However, these NN controllers either need off-line training or have too many parameters to regulate since they do not fully utilize the knowledge about pneumatic systems. Therefore, a combination of ARC control philosophy and NN is a practical way to improve the performance of pneumatic systems. A control scheme with NN based ARC [26; 27] was proposed for dealing with the unknown nonlinearities of the system and was applied to a linear motor. The mentioned NN based ARC suffered the difficulties of activation function selection, and the performance was not much better than ARC. A neural network learning ARC [28] controller with disturbances rejection was also synthesized for the industrial linear motor. Comparative experimental results showed better compensation of this data-driven RBF neural network when dealing with unmodeled dynamics and random disturbances.