Time-varying formation for linear multi-agent systems based on sampled data with multiple leaders

Abstract

This paper investigates the time-varying formation problem of a linear multi-agent system (MAS) based on sampled data with multiple leaders. The leader group and the follower group form the MAS. Followers are driven to reach the time-varying formation where the center of the formation is the convex combination of the states of the leaders. First, a time-varying formation control protocol with sampled data is proposed, while communication among followers is only occurred at sampling instants, which reduces the waste of communication energy significantly. Second, sufficient conditions for the MAS achieving the desired time-varying formation under sampling with multiple leaders are derived. In the theoretical analysis, a Lyapunov function is constructed to derive sufficient conditions based on formation protocol with sampled data for the MAS reaching time-varying formation. In addition, under formation control with sampled data, the problems of time-varying formation of MAS with one leader and time-invariant formation of MAS with multiple leaders are the special cases of the problem discussed in this paper. Finally, one example is presented to demonstrate the obtained theoretical analysis.