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In this article, the ultrafast tracking control for high-order discrete-time multiagent networks is investigated based on the predictive ability of agents. First, in view of the evolution of the original network dynamics, a distributed multistep prediction algorithm is established. Further, a control strategy containing predictive information is presented to achieve the ultrafast tracking control. Second, the problem of ultrafast tracking control with an $H_{\infty }$ performance specification is dealt with. The obtained result indicates that the robustness of the whole multiagent network can be converted into the robustness of multiple separable subsystems. Finally, the optimal ultrafast static tracking control design is provided for the single-integrator network with sampled dynamics. Two simulation cases are carried out to verify the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]