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.

中文翻译：

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多主体系统的固定时间同步共识控制

在本文中，定义了一个独特的多主体控制问题-所有主体状态的所有元素都同时达成共识，即，多主体系统实现时间同步共识和固定时间同步共识，其中同步的建立时间与多主体系统的初始状态无关。为了阐明此（固定）时间同步共识问题，我们首先提出时间同步稳定性和固定时间同步稳定性，这是一种特殊的固定/有限时间稳定性，其中系统状态的所有元素都同步到达同时平衡，同步稳定时间的上限取决于/不取决于初始条件。基于固定时间同步的稳定性，设计了一种无奇异的滑模控制律来解决固定时间同步共识问题。最后，进行了数值模拟以展示其有效性，并进一步探索了所提出控制器的优点。