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摘要: 针对发生执行器故障的多智能体系统, 论文提出一种新型分布式中间观测器的设计方法, 可以同时估计系统的状态和故障.本文设计的观测器可以应用于严格正实条件和观测器匹配条件不满足的系统.针对多智能体系统的通讯拓扑是有向图和无向图的情况, 分别获得估计误差系统稳定的条件.观测器的参数矩阵可以通过求解线性矩阵不等式(Linear matrix inequality, LMI)计算.针对具有有向拓扑的多智能体系统, 本文方法所需求解的LMI的维数, 等于对单个智能体系统设计观测器所需求解的LMI的维数.这表明应用本文方法进行故障估计时, 计算量不会随着系统中智能体数目的增加而增加.针对多智能体系统通讯拓扑是无向图的情况, 利用Laplacian矩阵的对称性, 可以得到保守性更小的结论.最后, 仿真算例验证了本文方法的有效性.Abstract: This paper focuses on the problem of robust distributed fault estimation for multi-agent systems with actuator faults. An intermediate observer design method is proposed to estimate the system states and faults simultaneously. The proposed observer can be used for the systems in which the strictly positive real condition and the observer matching condition are not satisfied. For the cases that the communication topology is a directed graph and an undirected graph respectively, sufficient conditions are obtained, which can ensure that the error systems are stable. The observer parameter matrices can be calculated utilizing the linear matrix inequality (LMI) technique. For the case that the communication topology is a directed graph, the dimension of the LMI needed to be solved is equal to that for the single agent system. This implies that the calculated amount remains unchanged even the number of agents increasing. For the case that the communication topology is an undirected graph, based on the symmetry of the Laplacian matrix, results with less conservative can be obtained. At last, simulation results are provided to illustrate the effectiveness of the proposed techniques.
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Key words:
- Multi-agent systems /
- distributed fault estimation /
- intermediate observer /
- linear matrix inequality (LMI)
1) 本文责任编委 潘泉 -
图 5 $\sqrt{\int_0^tY^{\rm T}(s)Y(s){\rm d}s}$和$\sqrt{\int_0^t\bar{\omega}^{\rm T}(s)\bar{\omega}(s){\rm d}s}$的比值
Fig. 5 The ratio of $\sqrt{\int_0^tY^{\rm T}(s)Y(s){\rm d}s}$ and $\sqrt{\int_0^t\bar{\omega}^{\rm T}(s)\bar{\omega}(s){\rm d}s}$
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