## 1 Introduction  
The exoskeleton refers to a wearable robot system comprising an external structural mechanism with joints and links corresponding to the human body [1]. With the initial advent of the exoskeleton robot, termed \"Hardiman\" and designed by the General Electric company born in 1960, people have quickly undertaken the development of wearable robot systems to assist and augment the force of human physical motions [2]. The Berkeley lower extremity exoskeleton (Bleex), the hybrid assistive limb, and the \"Mindwalker exoskeleton\" were designed for soldiers, nurses, and the elderly, respectively, to enhance their movement abilities and improve their loading limitation [3; 4; 5; 6]. In addition, these have been extensively used for robot-assisted rehabilitation therapy for the elderly or victims of stroke, spinal cord injury, and athletic injuries (e.g., SUEFUL-7 and EXO-7) [7; 8; 9]. As strongly demonstrated by related works, robot-rehabilitation exercises are capable of facilitating the recovery of the physical activity functions of patients, which can be longer lasting and repeatable [10; 11; 12; 13]. Moreover, upper-limb exoskeletons are primarily driven by servo motors (e.g., high radio reducers) or hydraulic systems with a bulky size, poor portability, as well as high joint stiffness. The actuator of the upper-limb exoskeleton should be a high power-to-weight ratio and exhibit a soft but flexible structure [14; 15; 16; 17]. To this end, a pneumatic artificial muscle (PAM) has been proposed for exoskeletons which is consistent with human muscles as it exhibits a flexible structure and is a rich carrier of energy [18; 19; 20; 21]. PAM is operated by air pressure. Its core element refers to a reinforced-closed membrane (i.e., bladder), which is radially expanding while axially contracting when inflated with air. In the upper-limb exoskeleton, PAM/PAMs can be deployed on the robot arm, exhibiting a unidirectional structure and an antagonistic structure [14]. However, several challenges exist which are hindering the adoption of PAM in exoskeleton robots. First, several researchers have highlighted that the PAM system exhibits time-varying features [22; 23]. Subsequently, as impacted by the elasticity of the bladder contained in the braided sheath and the mechanical characteristics (i.e., friction) between the bladder and the sheath combination under pressure, the PAM system is recognized as a nonlinear system [24; 25; 26; 27]. The mentioned challenges impose difficulties on the controller design for the high-performance position tracking system [28]. In recent years, the model-based control method has become a general method in the practice control of the PAM system [29]. The theoretical model (e.g., the quasi-static physical model) and the phenomenological model (e.g., the three-element model or the high-order linear model), i.e., the compensation model, were built to express the force-contraction behavior in the PAM control system [30; 31; 32]. However, the mentioned models contain several system and controller parameters, thereby increasing the difficulty in identification and complicating the building of an accurate model. For instance, five shape parameters and two air pressure parameters are required for calibrating in the quasi-static physical model of the McKibben type PAM [26]. To solve the mentioned issues, approximation structures (e.g., the fuzzy system or artificial neural network) were purposely employed in the PAM system [22; 33]. In addition, collecting accurate and sufficient data from the experiment lays a precondition for achieving the high performance of the mentioned approaches. Moreover, under the human impact, the external and uncertain disturbance dynamic model was capable of further affecting the accuracy of the model. Given the difficulties in building accurate models, several model-free control methods can act as the alternative means for the PAM system and exoskeleton [34].