||An adaptive Fourier neural network sliding mode controller with H ∞ tracking performance (AFNN-SMC+ H ∞) is applied for a Pneumatic actuator system (PAS) to overcome time-varying nonlinear dynamics and external disturbances. Benefiting from the use of orthogonal Fourier basis function, the proposed AFNN has fast estimated convergence speed; also, because AFNN has unique solution, it can avoid falling into the local minimum. The architecture of AFNN can also easily be determined by its clear physical meaning of the neurons. To attenuate the vibration of proportional directional control valve and the adaptive approximation error, the H ∞ tracking design technique is incorporated into the proposed AFNN-SMC. Finally, practical experiments are successfully implemented in position regulation, trajectory tracking, and velocity control of the PAS, which illustrates the effectiveness of the proposed controller.