Fully distributed adaptive consensus control of multi-agent systems with LQR performance index

This paper deals with fully distributed consensus control of linear multi-agent systems in continuous-time. The subsystems or the agents are connected by an undirected graph with unknown network connectivity, which is then estimated by a carefully designed adaptive scheme. With this adaptive scheme, the proposed control design only uses the relative state information of the subsystems in a neighbourhood. This makes the proposed control fully distributed, without the use of the network connectivity that requires the Laplacian matrix of the entire network. The proposed control is also guaranteed to achieve an optimal control performance index.