Interval consensus of variable quantity multi-agent systems under complex topology

Abstract

This paper deals with the complicated tracking problem with variable quantity agents. During the tracking process, the quantity of leader agent set and follower agent set are not fixed, this lead to the dimensions of tracking error and Laplacian dynamic are time-varying. Moreover, every agent imposes boundary condition on consensus value. Specifically, two kinds of interval constraints are introduced which driving system value to desired interval. Then, the consensus analysis becomes more difficult. To solve these issues, multiple Lyapunov functions are constructed to deal with the variable quantity multi-agent tracking process. By the way, we also deal with the finite time consensus with variable quantity agents. Finally, two examples are presented to verify the interval consensus and finite time consensus algorithms.