Distributed optimization design for second-order multi-agent systems

In this paper, we consider the dynamic optimization problem for continuous-time multi-agent systems with agents in the form of double integrators. Different from multi-agent consensus problem, we have to achieve an optimization performance when the agents become consensus. To solve the problem, we give a distributed gradient-based design for the considered multi-agent network under a connected interaction topology, and prove the convergence of the multi-agent systems to the optimization by Lyapunov techniques. Moreover, we also provide simulations to illustrate the theoretical results.