<p>This paper investigates the distributed finite-time optimization control problem for a class of uncertain heterogeneous high-order nonlinear multi-agent systems. These systems are subject to external disturbances and have immeasurable states. To address these issues, a systematic three-layer cooperative control framework is proposed. First, a practical finite-time fuzzy observer is developed to estimate the unmeasurable states. Simultaneously, a distributed finite-time optimal signal generator based on virtual first-order dynamics is constructed to obtain the global optimal solution. Subsequently, an adaptive practical finite-time tracking controller is designed via the backstepping technique, where a dynamic threshold-based event-triggered mechanism is introduced to alleviate the communication burden. Theoretical analysis demonstrates that the closed-loop system is semi-globally practical finite-time stable and all signals remain uniformly bounded. Finally, comparative simulations are carried out to verify the effectiveness of the proposed control scheme.</p>