<p>This paper investigates the consensus tracking control problem for high order nonlinear multi-agent systems subject to non-affine faults, partial measurable states, uncertain control coefficients, and unknown external disturbances. Under the directed topology conditions, an observer-based finite-time control strategy based on adaptive backstepping and is proposed, in which a neural network-based state observer is employed to approximate the unmeasurable system state variables. To address the complexity explosion problem associated with the backstepping method, a finite-time command filter is incorporated, with error compensation signals designed to mitigate the filter-induced errors. Additionally, the Butterworth low-pass filter is introduced to avoid the algebraic ring problem in the design of the controller. The finite-time stability of the closed-loop system is rigorously analyzed with the finite-time Lyapunov stability criterion, validating that all closed-loop signals of the system remain bounded within a finite time. Finally, the effectiveness of the proposed control strategy is verified through a simulation example.</p>