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Online learning, which involves incorporating newly acquired training data into GP models, promises to improve control performance by enhancing predictions during the operation. Therefore, this article investigates the online cooperative learning algorithm for MAS control. Moreover, an event-triggered data selection mechanism, inspired by the analysis of a centralized event-trigger (CET), is introduced to reduce the model update frequency and enhance the data efficiency. With the proposed learning-based control, the practical convergence of the MAS is validated with guaranteed tracking performance via the Lyapunov theory. Furthermore, the exclusion of the Zeno behavior for individual agents is shown. 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