A fuzzy finite-time optimal synchronization control method for a fractional-order permanent magnet synchronous generator, and belongs to the technical field of generators. A synchronization model between fractional-order driving and driven permanent magnet synchronous generators with capacitance-resistance coupling is established. The dynamic analysis fully reveals that the system has rich dynamic behaviors including chaotic oscillation, and a numerical method provides stability and instability boundaries. Then, under the framework of a fractional-order backstepping control theory, a fuzzy finite-time optimal synchronous control scheme which integrates a hierarchical type-2 fuzzy neural network, a finite-time command filter and a finite-time prescribed performance function is provided.