In this thesis, a radial basis function network (RBFN) based automatic generation fuzzy neural network (AGFNN) is proposed to control the rotor position of the permanent magnet linear synchronous motor (PMLSM) to track the period reference trajectories. The proposed RBFN based AGFNN not only has the advantages of the back-propagation algorithm, in which the parameter of the connected weights are adjusted but also has the advantages of the switching law, momentum term and RBFN, in which the tracking error and steady state responses will be betterment. The structure learning is based on the Mahalanobis distance and the parameter learning is based on the back-propagation algorithm. The simulation results of the proposed RBFN-based AGFNN, in which the periodic reference trajectories show that the tracking error and steady state responses are better performance, and the parameter variation and external load disturbance of system have robustness performance.