Leader-follower flocking control over signed communication networks

Existing fully distributed protocols for flocking are built upon the network of mobile agents with only cooperative interactions. Rather than investigating such networks, this paper deals with the problem of leader-follower flocking control over signed communication networks, where there impose less restrictions on the distributions of cooperations and competitions in the network of mobile agents. Firstly, for the second-order dynamics model, a novel state feedback controller that relies only on the relative velocity information of neighboring agents is developed. Secondly, the solvability of flocking control problem is transformed to the asymptotic stability of error system, and the latter is guaranteed by treating the product convergence of infinite super-stochastic matrices. Then, sufficient condition for the solvability of flocking control problem is proposed by establishing the inequality constraints on positive and negative edge weights. Finally, a numerical example is performed to illustrate the correctness of the theoretical result.