Distributed exponential finite-time coordination of multi-agent systems: containment control and consensus

Abstract

In this paper, exponential finite-time coordination problems of multi-agent systems are investigated, including containment control and consensus. The theoretical basis is that a class of nonlinear systems has favourable finite-time convergence characteristic. For the objective of containment control, the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time. For the objective of consensus, a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time. The distinguished features of this paper lie in the following two points: (1) a smaller settling time of the Lyapunov function is obtained, which manifests in a faster convergence rate than the traditional one and (2) the weakly connected topology considered in this paper is more general than the ones (a spanning tree, a spanning forest, and so on) in other coordination problems. All the results are illustrated by some simulations.

Keywords:

• multi-agent systems
• exponential finite-time
• containment control
• consensus
• pinning control

Acknowledgements

The authors would like to thank the editor, the associate editor and the reviewers for their valuable comments and suggestions.

Additional information

Funding

This work was supported in part by the National Nature Science Foundation of China [grant number 61273337], [grant number 61304170], [grant number 61225017], [grant number 61370032]; China Postdoctoral Science Foundation [grant number 2012M520459]; Beijing Nova Program [grant number Z121101002512066].