Fully Distributed Adaptive Scaled Consensus of Second-Order Multi-Agent Systems Under Directed Topology

This work primarily concentrate on the scaled consensus of second-order multi-agent systems in directed graph. Firstly, a novel lemma is proposed to realize scaled consensus. Secondly, the fully distributed adaptive controller is put forward based on local information of communication topology, which can adjust the weights of edges contained in directed spanning tree without the condition of knowing global information. The main challenge lies in designing proper adaptive laws to reach weight adjustment. Moreover, the developed adaptive strategy can be applied for any directed topology containing spanning trees, to achieve both leaderless and leader-following scaled consensus. Lastly, the numerical examples are cited to verify the availability of theoretical method.