基于有向图的信息拓扑独立的二阶系统一致性判据

针对可能存在拓扑切换情形的有向图, 研究了多个二阶系统在没有领航者时的一致性问题. 提出了两个使用不同合作策略的一致性算法, 并得到了若干与信息拓扑参数无关的一致性判据. 采用基于特征值分析的方法对第一个一致性算法进行了分析, 得到了该算法在固定有向图条件下一致性可达的充分必要条件. 对于第二个一致性算法, 如果切换网络拓扑的并图存在一棵有向生成树的频率足够高, 则系统仍然可以实现一致性. 利用等价模型变换将原系统转化为级联系统的方法, 给出并简化了该算法的收敛性分析. 采用同样的策略, 针对切换无向图的一致性问题进一步推导得到了一个新颖的充分必要条件. 另外, 本文还分别针对固定有向图研究了这两个算法对时延的鲁棒性. 论文最后给出了仿真示例, 验证了所得理论结果的正确性和算法的有效性.

Information Topology-independent Consensus Criteria for Second-order Systems under Directed Graph

In this paper, consensus seeking of second-order systems without leaders is investigated under possibly switching directed graphs. Two consensus algorithms using different cooperative schemes are proposed and some information topology-independent criteria are obtained. For the first one, an eigenvalue-based analysis is taken to attain a sufficient and necessary condition for consensus seeking under fixed directed graph. For the second one, consensus can be achieved as long as the union of the switching graphs has a directed spanning tree frequently enough. Convergence analysis is presented, which is facilitated by an equivalent model transformation into a cascaded system. A novel sufficient and necessary condition for consensus seeking under switching undirected graph is also obtained using the same strategy. Moreover, robustness of both the algorithms to time-delays is studied under fixed directed graph. Illustrative examples are also provided to show the effectiveness of the theoretical results.