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This paper focuses on the resource allocation problem(RAP) with constraints under a fixed general directed topology by using the distributed sub-gradient algorithm with event-triggered scheme in multi-agent systems, where each agent owns a cost function and its state value is bounded. The distributed sub-gradient algorithm aims to minimise the total cost by a distributed manner while achieving an optimal solution. Unlike centralised methods, the triggering condition and algorithm for each agent are fully decentralised. At each instant of time, each agent updates its state by employing the states which are collected from itself and its neighbouring agents at their last triggering time. In order to illustrate the effectiveness of the proposed sub-gradient algorithm with event-triggered control law, one simulation example is presented before the conclusion. [ABSTRACT FROM AUTHOR]