Department of Electrical Engineering, Indian Institute of Technology (BHU), Varanasi 221005, India.
School of Electronics, Electrical Engineering and Computer Science, Queen's University Belfast, Belfast BT9 6SB, UK.
Sensors (Basel). 2023 Apr 10;23(8):3865. doi: 10.3390/s23083865.
This paper deals with the predefined-time synchronization for a class of nonlinear multi-agent systems. The notion of passivity is exploited to design the controller for predefined-time synchronization of a nonlinear multi-agent system, where the time of synchronization can be preassigned. Developed control can be used to synchronize large-scale, higher-order multi-agent systems as passivity is an important property in designing control for complex control systems, where the control inputs and outputs are considered in determining the stability of the system in contrast to other approaches, such as state-based Control We introduced the notion of predefined-time passivity and as an application of the exposed stability analysis, static and adaptive predefined-time control algorithms are designed to study the average consensus problem for nonlinear leaderless multiagent systems in predefined-time. We provide a detailed mathematical analysis of the proposed protocol, including convergence proof and stability analysis. We discussed the tracking problem for a single agent, and designed state feedback and adaptive state feedback control scheme to make tracking error predefined-time passive and then showed that in the absence of external input, tracking error reduces to zero in predefined-time. Furthermore, we extended this concept for a nonlinear multi-agent system and designed state feedback and adaptive state feedback control scheme which ensure synchronization of all the agents in predefined-time. To further strengthen the idea, we applied our control scheme to a nonlinear multi-agent system by taking the example of Chua's circuit. Finally, we compared the result of our developed predefined-time synchronization framework with finite-time synchronization scheme available in literature for the Kuramoto model.
本文针对一类非线性多智能体系统的预定时间同步问题进行了研究。利用被动性的概念设计了非线性多智能体系统的预定时间同步控制器，其中可以预先指定同步时间。所开发的控制方法可用于同步大规模、高阶多智能体系统，因为被动性是设计复杂控制系统控制的重要特性，其中控制输入和输出被认为是确定系统稳定性的因素，而其他方法，如基于状态的控制，则不是。我们引入了预定时间被动性的概念，并作为所提出的稳定性分析的应用，设计了静态和自适应预定时间控制算法，以研究非线性无领导者多智能体系统在预定时间内的平均一致性问题。我们对所提出的协议进行了详细的数学分析，包括收敛证明和稳定性分析。我们讨论了单个智能体的跟踪问题，设计了状态反馈和自适应状态反馈控制方案，使跟踪误差在预定时间内被动，并证明在没有外部输入的情况下，跟踪误差在预定时间内减少到零。此外，我们将这个概念扩展到非线性多智能体系统，并设计了状态反馈和自适应状态反馈控制方案，以确保所有智能体在预定时间内同步。为了进一步加强这个想法，我们通过采用蔡氏电路的例子将我们的控制方案应用于非线性多智能体系统。最后，我们将我们开发的预定时间同步框架的结果与文献中可用的用于 Kuramoto 模型的有限时间同步方案进行了比较。
