| 引用本文: | 沈永明,朱旭,闫茂德.关于时滞车辆队列闭环稳定性的最紧要特征值[J].哈尔滨工业大学学报,2025,57(4):40.DOI:10.11918/202402003 |
| SHEN Yongming,ZHU Xu,YAN Maode.Most exigent eigenvalues for closed-loop stability of delayed vehicle platoons[J].Journal of Harbin Institute of Technology,2025,57(4):40.DOI:10.11918/202402003 |
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| 摘要: |
| 为研究时滞车辆队列的闭环稳定性与通信拓扑之间的本质关系揭示问题,针对二阶车辆队列与任意通信拓扑,提出了一种普适的最紧要特征值(MEE)搜寻方法。首先,基于车辆纵向动力学模型与含时滞分布式控制器,构建了时滞车辆队列闭环系统,并通过根趋势定义与Hermite稳定判据确定了系统仅存在一个时滞稳定区间。接着,对于拉普拉斯矩阵特征值全为实数的情况,通过分析系统最大容许时滞与拉普拉斯矩阵特征值之间的单调性关系,证明了二阶车辆队列的MEE必定为拉普拉斯矩阵的最大特征值。然后,对于部分特征值为共轭复数的情况,发现一对共轭复数特征值所对应的最大容许时滞大小相等,并给出了最大容许时滞的解析式。最后,在上述单调性关系分析过程中揭示了共轭复数特征值幅值与相角对MEE的影响规律,提出了简明的MEE搜寻规则。研究结果表明,通过仿真实例验证了所提理论方法的正确性,与传统遍历式的最大容许时滞求解方法相比,所提方法可大幅度降低运算量。MEE搜寻方法适用于任意通信拓扑下的二阶车辆队列系统闭环稳定性分析,具有普适性。 |
| 关键词: 时滞车辆队列 通信拓扑 最紧要特征值（MEE） 最大容许时滞 单调性分析 |
| DOI：10.11918/202402003 |
| 分类号:TP13 |
| 文献标识码:A |
| 基金项目:国家自然科学基金(4,6)；陕西省重点研发计划资助项目(2023YBGY398) |
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| Most exigent eigenvalues for closed-loop stability of delayed vehicle platoons |
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SHEN Yongming,ZHU Xu,YAN Maode
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(School of Electronics and Control Engineering, Chang’an University, Xi’an 710064, China)
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| Abstract: |
| To reveal the inherent relationship between the closed-loop stability of delayed vehicle platoons and communication topologies, a universal method of searching the most exigent eigenvalue (MEE) is proposed for second-order vehicle platoons under arbitrary communication topologies. First, for the case where all eigenvalues of the Laplacian matrix are real, by analyzing the monotonicity relationship between the maximum allowable delay and the eigenvalues, it is proven that the MEE of the second-order vehicle platoon must be the maximum eigenvalue of the Laplacian matrix. Then, for the case where some eigenvalues are complex conjugates, it is found that the maximum allowable delays corresponding to a pair of complex conjugate eigenvalues are equal in size, and an analytical expression for the maximum allowable delay is provided. Furthermore, during the analysis of the aforementioned monotonic relationship between the maximum allowable delay and the eigenvalues, the influence of the magnitude and phase of the complex conjugate eigenvalues on the MEE is revealed, and a concise MEE search rule is proposed. The results show that the proposed theoretical method is validated through simulation examples. Compared with traditional traversal methods of calculating the maximum allowable delay, the proposed method significantly reduces the computational burden. This method of searching the MEE is applicable to the closed-loop stability analysis of second-order vehicle platoons under arbitrary communication topologies and demonstrates universality. |
| Key words: delayed vehicle platoon communication topology most exigent eigenvalue（MEE） maximum allowable delay monotonicity analysis |
