This paper revisits the problem of global optimal consensus by bounded controls for a multi-agent system, where each agent is described by the dynamics of chains of integrators and has its own objective function known only to itself. A bounded local control law is constructed that uses the information accessible to it through the communication topology underlying the multi-agent system and the information of its own objective function. Under the assumption that the communication topology is strongly connected and detailed balanced, these control laws together achieve global optimal consensus for the multi-agent system, that is, all agents reaching consensus at a state that minimizes the sum of the objective functions of all agents. A numerical example illustrates the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.