Parameterization of all distributed controllers based on gradient-flow method for networked multi-agent systems

In this paper, a parameterization of all distributed controllers based on the gradient-flow method is presented for networked multi-agent systems. In the gradient-flow method, the cooperative controllers are uniquely determined from the gradients of objective functions which correspond to control tasks. However, these controllers are not necessarily distributed. Hence, we parameterize all objective functions whose gradients are appropriate for distributed control. It turns out that cliques (i.e., complete induced subgraphs) play a crucial role to obtain all distributed controllers. This is in contrast to the conventional objective functions, which depend on edges instead of cliques. Based on this parameterization, the distributed controllers can be obtained automatically just by choosing free parameters. A controller design example is given to demonstrate the effectiveness of the proposed method, where it is shown that this method enhances the control performance compared to the conventional method.