<p>This paper proposes two novel distributed predefined-time algorithms to solve the dynamic weighted average tracking control problem of first-order multi-agent systems. The first algorithm, a distributed accurate predefined-time algorithm, guarantees that the system state precisely tracks the time-varying weighted average signal within a predefined time. The second, a distributed bounded predefined-time algorithm, ensures that tracking errors converge to a bounded region within a predefined time. Additionally, this paper introduces a novel globally predefined-time stability theory for nonlinear systems. Leveraging this theory, we conduct a thorough analysis of the predefined-time convergence of our proposed algorithms. Finally, the effectiveness and superiority of our algorithms are validated through rigorous performance evaluations and engineering applications.</p>