Distributed Connectivity-Preserving Control Design With Fast Convergence Over Directed Communication Topology

Abstract

This work addresses the consensus problem for first-order multiagent systems with fixed-time convergence rate and heterogeneous communication range constraints. A novel class of distributed fixed-time consensus control algorithms is proposed with connectivity preservation property over directed graphs for nominal agents. Then, the proposed protocol is modified to solve the fixed-time connectivity-preserving consensus for nonlinear and disturbed multiagent systems. The edge-based representation framework is utilized and two strict Lyapunov functions are constructed to show that the initial edges can be maintained under the proposed control protocols. Furthermore, the fixed-time consensus is achieved, where all of the states reach a common value within a finite time, which is upper bounded regardless of initial states. Consequently, the convergence time can be set in advance. Two numerical examples are performed to illustrate the proposed schemes.