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摘要:
针对一类Lipschitz非线性多智能体系统的一致性控制问题，在一般有向拓扑条件下，研究了通信网络具有不确定性的一致性控制方法，设计了基于输出反馈的一致性控制器。利用拓扑图拉普拉斯矩阵的性质，克服了有向拓扑不对称性的影响，将有向拓扑条件下的一致性控制问题转化为低维非线性系统的鲁棒镇定问题；利用李雅普诺夫函数直接方法，推导系统达成一致的充分性条件，将控制器反馈矩阵的设计转化为求解线性矩阵不等式可行解问题。分别在无领导者和有领导者2种拓扑条件下进行数值仿真，结果表明：系统在通信网络存在不确定性时可以达成一致性。
Abstract:Under general directed topology conditions, a consensus control approach with uncertainty in communication networks is studied, and a consensus controller based on output feedback is built, with the aim of solving the consensus control problem of a class of Lipschitz nonlinear multi-agent systems. Based on the properties of the Laplacian matrix of a graph, the influence of asymmetric topology is overcome, and the consensus control problem under the condition of directed topology is transformed into a robust stabilization problem of a dimension-reduced nonlinear system. Using the properties of the Laplacian matrix,we overcome the influence of asymmetric topology,and convert the consensus control problem under the condition of directed topology into a resilient stabilization problem of a dimension-reduced nonlinear system. Using the Lyapunov function direct method, the sufficiency conditions for the system to achieve consensus are deduced, and the design of the feedback matrix of the controller is transformed into a feasible solution problem for solving linear matrix inequalities. Finally, numerical simulations were conducted under both leaderless and leader-following topology conditions, and the results showed that the system can achieve consensus in the presence of uncertainty in the communication network.
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Key words:
- network uncertainty /
- consensus /
- nonlinear /
- multi-agent systems /
- output feedback
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图 2 智能体状态分量$ {x_{i1}}(i = 1,\cdots ,6 )$的变化曲线（例1）
Figure 2. variation curves of agent state component $ {x_{i1}}(i = 1,\cdots ,6) $
图 3 智能体状态分量$ {x_{i2}}(i = 1,\cdots ,6) $的变化曲线（例1）
Figure 3. variation curves of agent state component $ {x_{i2}}(i = 1,\cdots ,6) $
图 4 智能体状态分量$ {x_{i3}}(i = 1,\cdots ,6) $的变化曲线（例1）
Figure 4. variation curves of agent state component $ {x_{i3}}(i = 1,\cdots ,6) $
图 5 智能体状态分量$ {x_{i4}}(i = 1,\cdots ,6) $的变化曲线（例1）
Figure 5. variation curves of agent state component $ {x_{i4}}(i = 1,\cdots ,6) $
图 6 智能体状态误差分量$ {\xi _{i1}}(i = 1,\cdots ,5) $的变化曲线（例1）
Figure 6. variation curves of agent state error component $ {\xi _{i1}}(i = 1,\cdots ,5) $
图 7 智能体状态误差分量$ {\xi _{i2}}(i = 1,\cdots ,5) $的变化曲线（例1）
Figure 7. variation curves of agent state error component $ {\xi _{i2}}(i = 1,\cdots ,5) $
图 8 智能体状态误差分量$ {\xi _{i3}}(i = 1,\cdots ,5) $的变化曲线（例1）
Figure 8. variation curves of agent state error component $ {\xi _{i3}}(i = 1,\cdots ,5) $
图 9 智能体状态误差分量$ {\xi _{i4}}(i = 1,\cdots ,5) $的变化曲线（例1）
Figure 9. variation curves of agent state error component $ {\xi _{i4}}(i = 1,\cdots ,5) $
图 11 智能体状态分量$ {x_{i1}}(i = 1,\cdots ,6) $的变化曲线（例2）
Figure 11. variation curves of agent state component $ {x_{i1}}(i = 1,\cdots ,6 )$
图 12 智能体状态分量$ {x_{i2}}(i = 1,\cdots ,6) $的变化曲线（例2）
Figure 12. variation curves of agent state component $ {x_{i3}}(i = 1,\cdots ,6) $
图 13 智能体状态分量$ {x_{i3}}(i = 1,\cdots ,6) $的变化曲线（例2）
Figure 13. variation curves of agent state component $ {x_{i3}}(i = 1,\cdots ,6) $
图 14 智能体状态分量$ {x_{i4}}(i = 1,\cdots ,6) $的变化曲线（例2）
Figure 14. variation curves of agent state component $ {x_{i4}}(i = 1,\cdots ,6) $
图 15 智能体状态误差分量$ {\xi _{i1}}(i = 1,\cdots ,5) $的变化曲线（例2）
Figure 15. variation curves of agent state error component $ {\xi _{i1}}(i = 1,\cdots ,5) $
图 16 智能体状态误差分量$ {\xi _{i2}}(i = 1,\cdots ,5) $的变化曲线（例2）
Figure 16. variation curves of agent state error component $ {\xi _{i2}}(i = 1,\cdots ,5) $
图 17 智能体状态误差分量$ {\xi _{i3}}(i = 1,\cdots ,5) $的变化曲线（例2）
Figure 17. variation curves of agent state error component $ {\xi _{i3}}(i = 1,\cdots ,5) $
图 18 智能体状态误差分量$ {\xi _{i4}}(i = 1,\cdots ,5) $的变化曲线（例2）
Figure 18. variation curves of agent state error component $ {\xi _{i4}}(i = 1,\cdots ,5) $
图 19 误差分量$ {\xi _{i1}}(i = 1,\cdots ,5) $的变化曲线(第1组)
Figure 19. Variation curves of error component (group 1) $ {\xi _{i1}}(i = 1,\cdots ,5) $
图 20 误差分量$ {\xi _{i1}}(i = 1,\cdots ,5) $的变化曲线(第2组)
Figure 20. Variation curves of error component (group 2) $ {\xi _{i1}}(i = 1,\cdots ,5) $
图 21 误差分量$ {\xi _{i1}}(i = 1,\cdots ,5) $的变化曲线(第3组)
Figure 21. Variation curves of error component (group 1) $ {\xi _{i1}}(i = 1,\cdots ,5) $
表 1 不同参数条件下不等式(7)可解性对比
Table 1. Comparison of solvability of inequality (7) under different parameter conditions
序号 b1 b2 b3 b4 b5 b6 $ {\delta _0} $ 可解性 1 0.006 −0.02 0.03 −0.01 0.05 −0.001 0.05 不可解 2 0.01 −0.02 0.03 −0.01 0.04 −0.001 0.02 不可解 3 0.01 −0.009 0.003 −0.006 0.01 −0.009 0.01 可解 4 0.002 −0.003 0.003 −0.001 0.002 −0.001 0.003 可解 
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