H ∞ control of networked multi-agent systems

This paper concerns the disturbance rejection problem arising in the coordination control of a group of autonomous agents subject to external disturbances. The agent network is said to possess a desired level of disturbance rejection, if the H _∞ norm of its transfer function matrix from the disturbance to the controlled output is satisfactorily small. Undirected graph is used to represent the information flow topology among agents. It is shown that the disturbance rejection problem of an agent network can be solved by analyzing the H _∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. An interesting result is that the disturbance rejection ability of the whole agent network coupled via feedback of merely relative measurements between agents will never be better than that of an isolated agent. To improve this, local feedback injections are applied to a small fraction of the agents in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. Finally, extensions to the case when communication time delays exist are also discussed. This research is supported by the Natural Science Foundation of China under Grants Nos. 10832006 and 60674093.