On multi-agent self-tuning consensus

This paper considers the consensus problem in complex networks of uncertain discrete time agents. The coupling parameters among agents are locally self tuned by least-mean square (LMS) algorithm, without using any global information. In this process each agent minimizes a local cost function dependent on the error between the agent state and the average of neighbors states. Provided that the network graph is strongly connected, it is shown that for each agent the sequence of coupling parameters is convergent, and all agent states converge toward the same constant value. It is demonstrated that in the face of unknown high-frequency gain, the proposed algorithms generate such coupling parameters so that the overall multi-agent system is marginally stable with only one pole on the unit circle, located at λ=1.