Liu Jason J R, Lam James, Kwok Ka-Wai
IEEE Trans Neural Netw Learn Syst. 2023 Nov;34(11):9542-9548. doi: 10.1109/TNNLS.2022.3152939. Epub 2023 Oct 27.
This article investigates the positive consensus problem of a special kind of interconnected positive systems over directed graphs. They are composed of multiple fractional-order continuous-time positive linear systems. Unlike most existing works in the literature, we study this problem for the first time, in which the communication topology of agents is described by a directed graph containing a spanning tree. This is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains, which renders the positivity analysis fairly challenging. Based on the existing results in spectral graph theory, fractional-order systems (FOSs) theory, and positive systems theory, we derive several necessary and/or sufficient conditions on the positive consensus of fractional-order multiagent systems (PCFMAS). It is shown that the protocol, which is designed for a specific graph, can solve the positive consensus problem of agents over an additional set of directed graphs. Finally, a comprehensive comparison study of different approaches is carried out, which shows that the proposed approaches have advantages over the existing ones.
本文研究了一类特殊的有向图上互联正系统的正一致性问题。它们由多个分数阶连续时间正线性系统组成。与文献中大多数现有工作不同，我们首次研究这个问题，其中智能体的通信拓扑由包含生成树的有向图描述。由于拉普拉斯矩阵的特征值与控制器增益之间的相互作用，这是一个更一般且新颖的场景，这使得正性分析颇具挑战性。基于谱图理论、分数阶系统（FOSs）理论和正系统理论的现有结果，我们推导了分数阶多智能体系统正一致性（PCFMAS）的几个必要和/或充分条件。结果表明，为特定图设计的协议可以解决智能体在另外一组有向图上的正一致性问题。最后，对不同方法进行了全面的比较研究，结果表明所提出的方法优于现有方法。
