Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics

ABSTRACT

This paper is concerned with finite-time and fixed-time consensus of multi-agent systems in a leader-following framework. Different from conventional leader-following tracking approaches where inherent dynamics satisfying the Lipschitz continuous condition is required, a more generalised case is investigated: discontinuous inherent dynamics. By nonsmooth techniques, a nonlinear protocol is first proposed to achieve the finite-time leader-following consensus. Then, based on fixed-time stability strategies, the fixed-time leader-following consensus problem is solved. An upper bound of settling time is obtained by using a new protocol, and such a bound is independent of initial states, thereby providing additional options for designers in practical scenarios where initial conditions are unavailable. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

KEYWORDS:

• Finite-time consensus
• fixed-time consensus
• discontinuous inherent dynamics
• multi-agent systems
• distributed control

Acknowledgment

The authors would like to thank the Senior Editor and three anonymous reviewers for their valuable comments that improved the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.