带延迟的分数阶非线性领导-跟随系统中的稳健共识分析:结合实用控制器设计和非线性动力学

Asad Khan, Muhammad Awais Javeed, A. U. K. Niazi, Saadia Rehman, Yubin Zhong
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摘要

本文研究了具有分布和输入滞后的分数阶非线性领导-跟随系统的基于弹性的共识分析。为了提高控制器设计的实用性,本文提出了一个扰动项。我们的建模框架提供了一种更精确、更灵活的方法,通过利用分数微积分考虑了代理动态的记忆和遗传方面。此外,系统的领导者和追随者方程还加入了非线性函数,以探索由此产生的变化。领导者-追随者系统由加权图表示,加权图可以是无向图,也可以是有向图。利用代数图论和分数阶拉祖米欣技术进行分析,以代数方式呈现了领导者-跟随者共识的情况。为了提高多代理系统的鲁棒性,使用了输入和分配延迟来适应通信延迟并复制实时变化的环境。本研究为开发复杂网络系统中更稳健、更灵活的控制方法奠定了基础。它通过推进我们对分数阶多代理系统的理解和实际应用来实现这一目标。此外,我们还进行了实验,以展示该设计在系统内达成共识的有效性。
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Robust Consensus Analysis in Fractional-Order Nonlinear Leader-Following Systems with Delays: Incorporating Practical Controller Design and Nonlinear Dynamics
This article investigates the resilient-based consensus analysis of fractional-order nonlinear leader-following systems with distributed and input lags. To enhance the practicality of the controller design, an incorporation of a disturbance term is proposed. Our modeling framework provides a more precise and flexible approach that considers the memory and heredity aspects of agent dynamics through the utilization of fractional calculus. Furthermore, the leader and follower equations of the system incorporate nonlinear functions to explore the resulting changes. The leader-following system is expressed by a weighted graph, which can be either undirected or directed. Analyzed using algebraic graph theory and the fractional-order Razumikhin technique, the case of leader-following consensus is presented algebraically. To increase robustness in multi-agent systems, input and distributive delays are used to accommodate communication delays and replicate real-time varying environments. This study lays the groundwork for developing control methods that are more robust and flexible in complex networked systems. It does so by advancing our understanding and practical application of fractional-order multi-agent systems. Additionally, experiments were conducted to show the effectiveness of the design in achieving consensus within the system.
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