切换拓扑下的Conformable分数阶多智能体系统的领导-跟随一致性

摘要/Abstract

摘要： 由于分数阶Caputo定义或分数阶Riemann-Liouille(R-L)固有的记忆特性和非局部效应,在进行拓扑切换时Caputo和R-L分数阶的积分下界无法随着拓扑的切换而被更新,意味着在不同的区间内不能直接取分数阶导数的分数阶积分(为确保历史信息不受切换影响).为了克服这些困难,引入Conformable分数阶导数.通过Conformable分数阶算子理论,利用多Lyapunov函数方法和平均驻留时间方法给出了切换拓扑下的Conformable分数阶多智能体系统领导-跟随一致性渐近可达的充分条件,并设计了相应的切换信号.最后,通过2个实际例子仿真验证了所得理论结果的有效性和实用性,并且与整数阶的情形作了比较.

关键词: 多智能体系统, Conformable分数阶, 切换拓扑, 平均驻留时间, 多Lyapunov函数

Abstract: Due to the inherent memory characteristics and non-local effects of the fractional-order Caputo and Riemann-Liouville (R-L) definitions, during topology switching, the integral bounds of the Caputo and R-L fractional orders cannot be updated to match the topology changes, preventing fractional derivatives from being directly applied over different intervals, thereby preserving historical information despite the topology switch. To overcome these difficulties, the Conformable fractional derivative is introduced, which is derived from the limited definition of integer-order derivatives. Utilizing the conformable fractional operator theory, along with the multiple Lyapunov function method and the average dwell-time technique, sufficient conditions are established to ensure the asymptotic leader-follower consensus of conformable fractional-order multi-agent systems under switching communication topologies. Furthermore, an appropriate switching signal is designed to satisfy the proposed conditions. Finally, two simulation examples are provided to verify the effectiveness and practicality of the theoretical results, and comparative analyses with corresponding integer-order systems are conducted to illustrate performance advantages of the proposed framework.

Key words: multi-agent systems, Conformable fractional, switching topologies, average dwell time, multiple Lyapunov function

中图分类号:

TP18

任礼辉, 龙飞, 杨慧, 周健平. 切换拓扑下的Conformable分数阶多智能体系统的领导-跟随一致性[J]. 兰州理工大学学报, 2026, 52(2): 79-90.

REN Li-hui, LONG Fei, YANG Hui, ZHOU Jian-ping. Leader-follower consensus of Conformable fractional order multi-agent systems based in switching topology[J]. Journal of Lanzhou University of Technology, 2026, 52(2): 79-90.

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链接本文: https://journal.lut.edu.cn/CN/

https://journal.lut.edu.cn/CN/Y2026/V52/I2/79

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