有向切换拓扑下非线性多智能体系统的一致性控制

本文研究有向切换拓扑条件下无领导者的Lur'e型非线性多智能体系统的动态一致性问题。设计了基于协同邻居输出信息的观测器类型的动态一致性算法，可以保证在邻居状态信息未知情况下系统达到一致。利用Laplacian矩阵的特殊性质以及Laplacian矩阵的降维变型形式，提出了一种新的拓扑依赖的多重Lyapunov函数构建方法，进而将切换拓扑下的一致性问题转换为低维切换系统的稳定性问题。该方法放宽了对拓扑条件的约束，实现了网络拓扑依赖矩阵和系统动态依赖矩阵的独立设计。再利用多重Lyapunov函数法结合线性矩阵不等式方法对系统进行稳定性分析，给出动态一致性控制器的反馈矩阵的求解方法，得到了平均驻留时间条件。结果表明，提出的方法可使得Lur'e型非线性多智能体系统达成一致，只要满足每个候选拓扑中都包含有向生成树且切换拓扑的平均驻留时间大于一个指定的阈值。

Consensus of nonlinear multi-agent systems with directed switching topologies

This paper addresses the dynamic consensus problem of Lur'e-type nonlinear multi-agent systems with directed switching topologies. Distributed dynamic consensus controllers are designed based on relative output information of neighboring agents. The special property of the directed graph Laplacian matrix is used to decompose the Laplacian matrix and the linear transformation in a particular form is adopted to convert the consensus problem with switching topologies into a stabilization problem of a switched system with lower dimensions. The piecewise continuous Lyapunov function is proposed to analyze the equivalent system by solving linear matrix inequalities. A design method is proposed to properly select the controller gains, and the average dwell time condition is obtained. Finally, simulation is conducted to illustrate the effectiveness of the theoretical results.