Formation control for high-order linear swarm systems with complex communication conditions
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摘要:
针对时变时延、拓扑不确定和外部扰动等复杂通信条件下的高阶线性群系统编队控制问题进行研究。首先，建立了群系统编队控制问题的数学描述，并基于一致性最近邻原则给出了编队控制协议框架。其次，提出了群系统实现编队的充要条件。通过状态分解和变量代换，给出了约束条件下，编队控制协议的设计方法。同时，为得到群系统所允许最大时延边界，引入自由权矩阵，得到了保守性较小的线性矩阵不等式（LMI）判据条件。仿真实验验证了编队控制方法对于有界时变时延、拓扑不确定以及外部扰动具有一定的鲁棒性。
Abstract:The formation control problems for high-order linear swarm systems with time-varying delays, topology uncertainties and external disturbances are investigated. Firstly, the mathematical description of the formation control for swarm systems is established, and the formation control protocol is proposed based on the consensus nearest neighbor principle. Secondly, the necessary and sufficient conditions for swarm systems to achieve the formation are presented. By decomposing the state and using the variable substitution method, the design method of formation protocol is given under the constrained conditions. Furthermore, in order to get the upper bound of the time-varying delays, the free-weighting matrices are introduced, and the linear matrix inequality (LMI) criteria with lower conservation are obtained. Finally, numerical examples and simulation results are given to demonstrate the effectiveness of the proposed method. The formation control method is robust for bounded time-varying delays, topology uncertainties and external disturbances.
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图 2 8个主体的状态和c(t)的状态在不同时刻的截图
Figure 2. Snapshot of states of eight agents and c(t) at different moments
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