Fixed-Time-Synchronized Consensus Control of Multiagent Systems

In this article, a unique multiagent control problem is defined-all the elements of all the agent states reaching consensus at the same time, i.e., the multiagent system achieves time-synchronized consensus and fixed-time-synchronized consensus, where the upper bound of the synchronized settling time is independent of the initial states of multiagent systems. To articulate this (fixed-) time-synchronized consensus problem, we first propose time-synchronized stability and fixed-time-synchronized stability, a special kind of fixed/finite-time stability, where all the elements of the system state synchronously arrive at the equilibrium at the same time, with the upper bound of the synchronized settling time dependent/independent of initial conditions. Based on fixed-time-synchronized stability, a singularity-free sliding mode control law is designed to solve the fixed-time-synchronized consensus problem. Finally, numerical simulations are conducted to showcase the effectiveness, and further exploration of the merit of the proposed controller is provided.