Pneumatic artificial muscles (PAMs) have been widely used in actuation of medical devices due to their intrinsic compliance and high power to weight ratio features. However, the nonlinearity and time-varying nature of PAMs makes it challenging to maintain highperformance tracking control. In this paper, a High-Order Pseudo-Partial Derivative based Model-Free Adaptive Iterative Learning Controller (HOPPD-MFAILC) is proposed to achieve fast convergence speed. The dynamics of PAM is converted into a dynamic linearization model during iterations, meanwhile, a high-order estimation algorithm is designed to estimate the pseudo-partial derivative component of the linearization model by only utilizing the input and output data in previous iterations. The stability and convergence performance of the controller is verified through theoretical analysis. Simulation and experimental results on PAM demonstrate that the proposed HOPPD-MFA ILC can track the desired trajectory with improved convergence and tracking performance. Index Terms-Pneumatic artificial muscle, model-free adaptive control, iterative learning control, convergence. I. INTRODUCTION NEUMATIC artificial muscle (PAM) is a tube-like actuator that largely mimics biological human muscle functions [1]. Compared to traditional electrical motors and hydraulic actuators, the lightweight, high compliance and high power-to-weight ratio of PAMs [2] have fueled their popularity among assistive exoskeletons and rehabilitation robots, such as the upper limb exoskeleton series RUPERT [3] and the lower limb orthotics KAFO [4]. However, unlike the conventional actuators adopted in Lokomat [5] and ArmeoPower [6], the nonlinear and time-varying nature of PAMs may cause Manuscript