Cao Yongcan, Li Yan, Ren Wei, Chen YangQuan
Department of Electrical and Computer Engineering, Utah State University, Logan, UT 84322 USA.
IEEE Trans Syst Man Cybern B Cybern. 2010 Apr;40(2):362-70. doi: 10.1109/TSMCB.2009.2024647. Epub 2009 Jul 7.
This paper studies the distributed coordination of networked fractional-order systems over a directed interaction graph. A general fractional-order coordination model is introduced by summarizing three different cases: 1) fractional-order agent dynamics with integer-order coordination algorithms; 2) fractional-order agent dynamics with fractional-order coordination algorithms; and 3) integer-order agent dynamics with fractional-order coordination algorithms. We show sufficient conditions on the interaction graph and the fractional order such that coordination can be achieved using the general model. The coordination equilibrium is also explicitly given. In addition, we characterize the relationship between the number of agents and the fractional order to ensure coordination. Furthermore, we compare the convergence speed of coordination for fractional-order systems with that for integer-order systems. It is shown that the convergence speed of the fractional-order coordination algorithms can be improved by varying the fractional orders with time. Finally, simulation results are presented as a proof of concept.
本文研究了有向交互图上网络化分数阶系统的分布式协调。通过总结三种不同情况引入了一个通用的分数阶协调模型：1）具有整数阶协调算法的分数阶智能体动力学；2）具有分数阶协调算法的分数阶智能体动力学；3）具有分数阶协调算法的整数阶智能体动力学。我们给出了交互图和分数阶上的充分条件，使得可以使用通用模型实现协调。还明确给出了协调平衡点。此外，我们刻画了智能体数量与分数阶之间的关系以确保协调。而且，我们比较了分数阶系统与整数阶系统协调的收敛速度。结果表明，通过随时间改变分数阶可以提高分数阶协调算法的收敛速度。最后，给出仿真结果作为概念验证。
