Li Xue, Yu Zhiyong, Jiang Haijun
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
Entropy (Basel). 2021 Oct 27;23(11):1412. doi: 10.3390/e23111412.
In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.
本文研究了具有外部干扰的一阶非线性多智能体系统（FONMASs）的领导者-跟随者一致性问题。首先，设计了一种新颖的分布式固定时间滑模流形，并提出了一种基于一般有向图的新型静态事件触发协议，该协议能够很好地抑制外部干扰，使FONMASs在固定时间内实现领导者-跟随者一致性。基于固定时间稳定性理论和不等式技术，得到了控制参数需满足的条件，并可避免芝诺行为。此外，我们改进了所提出的协议，为具有多个领导者的FONMASs提出了一种新的事件触发策略。如果精心设计控制参数，系统能够在固定时间内到达滑模面并实现包容控制。最后，给出了几个数值模拟结果以验证所提协议的有效性。
