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In this paper, an observer-based command filtered adaptive neural network tracking control problem is addressed for a fractional-order chaotic permanent magnet synchronous motor (PMSM) with the immeasurable state, parameter uncertainties, and external load disturbance. First, the Chebyshev neural networks are introduced to approximate the nonlinear and unknown functions. Next, a neural network reducedorder state observer is designed to obtain the unmeasured state. Then, the command filtering approach based on the first-order Levant differentiator is developed to solve the ''explosion of complexity'' issue of backstepping, and a novel fractional-order error compensation mechanism is employed, which can remove the filtering errors in finite time. After that, the continuous frequency distributed model is investigated to design proper Lyapunov function, and it is demonstrated that the proposed control method not only ensures that all signals in the fractional-order PMSM system are bounded but also suppresses chaotic oscillation. Finally, the simulation studies are provided to verify the correctness and effectiveness of the proposed scheme.

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