The consensus control with optimal cost remains major challenging although consensus control problems have been well studied in recent years. In this paper, we study the consensus control of a multi-agent system associated with a given cost function. The main contribution is to present the distributed control protocol while minimizing the given cost function with positive semi-definite weighting matrix of control based on the regular/irregular optimal control. The derived controller is composed of two parts: One part is the feedback of the individual state which minimizes the cost function and the other part is the feedback of the relative states between the neighbours which guarantees the consensus. The presented results are novel to the best of our knowledge.