Distributed optimization problem for second-order multi-agent networks with only position interaction

In this paper, distributed optimization problem is investigated under a second-order multi-agent network, in which each agent is described as the double integrator. The multi-agent network is introduced for solving a large scale optimization problem by the cooperation of coupled agents. Based on the interaction over the network, the optimal solution of the problem can be obtained. Since the existing distributed algorithms for second-order multi-agent network enforce each agent to transmit complete information (both state information and derivation information of the independent variable, i.e., corresponded position and velocity information of the agent), this paper is motivated to design the distributed algorithm with only using the position information of neighbors, which reduces the requirement on communication bandwidth. With the help of Lyapunov analysis and LaSallel's Invariance Principle, the optimal solution is derived and the optimization problem is solved via the second-order multi-agent network. Finally, a numerical example is presented to illustrate the theoretical result.