Distributed control gains design for second-order consensus in multi-agent systems with matrix-weighted networks

In this paper, the consensus problems of second-order multi-agent systems are investigated. In particular, matrix-weighted networks are applied to show the interdependence of multi-dimensional position and velocity information between neighbouring agents. First, an effective distributed control protocol with fixed control gains which does not depend on the relationship between the position coupling gain and the velocity coupling gain is designed to ensure that the system can achieve global consensus. Besides of consensus, cluster consensus is also considered. Then, in order to significantly improve the convergence speed of second-order multi-agent systems, a novel consensus protocol is designed by introducing two adaptive control gains and proposing an efficient distributed adaptive-gain design strategy. Finally, numerical simulations are presented to confirm the correctness and validity of our conclusions.