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This paper studies the cooperative optimal control for multi-agent systems (MASs) with Lipschitz nonlinearities over general digraphs. The leader-following consensus model consisting of multiple followers and one leader is constructed. Distributed optimal control protocols using the linear quadratic regulator approach are designed. Under the proposed protocols, the performance index of the MAS is optimized by solving the algebraic Riccati equation (ARE). The weighting matrices of performance index rely on the Lipschitz nonlinearities, leading to optimal performance. Simulation studies are finally reported to illustrate the effectiveness of presented protocols.