Distributed Optimal Consensus of Second-order MASs over Directed Graphs*

The optimal consensus problem (OCP) for multiagent systems (MASs) is addressed in this paper. The dynamics of agents are second-order. These agents communicate with the neighbors through a directed graph. It is assumed to be strongly connected and weight-balanced. In the system, each agent has a local private cost function. The global cost function is the sum of those local cost functions. In order to address such OCP, based on the tracking method, a novel distributed control strategy is proposed. The state information (position or velocity) of the agents does not need to be communicated with the neighbors, which implies that the proposed control strategy can protect the real state information to be known by the neighbors to some extent. Under assumptions that the local private cost function are strongly convex and continuously differentiable with Lipschitz continuous gradients, the sufficient criteria are given, under which the positions of all agents controlled by the designed controllers can achieve consensus on the optimal solution of the global cost function exponentially. Finally, two simulation examples are provided to illustrate the efficiency of the designed distributed control strategy.