The vehicle platoon using the cooperative adaptive cruise control (CACC) transmits information between vehicles via communication networks to increase the control performance. However, time delays are inevitable during the network transmission of information, which influence the stability of the CACC vehicle system. This paper proposes a method for compensating information affected by time delays based on a Bi-LSTM model. First, the third-order dynamics of the CACC vehicle systems are established, and the control strategies are proposed with the leading, preceding and following vehicles. The conditions of local stability and string stability for the CACC vehicle systems without time delays are derived based on the Routh-Hurwitz stability criterion and the frequency domain methods, which reveal the relationship between the model parameters and the controller parameters. For the CACC vehicle systems with time delays, the maximum time delays that ensure the local stability and string stability are achieved using the similar methods accordingly. However, the stability of the CACC vehicle systems is destroyed, when the time delay exceeds the maximum value. To deal with the impact of time delays, the bidirectional long short term memory (Bi-LSTM) model is adopted to predict and reconstitute the information affected by time delays. Furthermore, the relevant parameters are set and the real vehicle data is used for calculation and simulation. The simulation results confirm the local and string stability can be ensured, and further show the boundary of the maximum time delay may reach 0.45s for the CACC vehicle systems in this paper. In order to highlight superiority of Bi-LSTM, by comparing LSTM and KF with BiLSTM, the simulation results show Bi-LSTM has the highest correlation coefficient and the smallest root mean square error, which verify that Bi-LSTM reconstructing information affected by time delays is more effective than KF and LSTM.

中文翻译：

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基于 Bi-LSTM 的 CACC 系统稳定性与时间延迟和车辆补偿延迟的重构信息


使用协同自适应巡航控制 （CACC） 的车辆列队通过通信网络在车辆之间传输信息，以提高控制性能。然而，在信息网络传输过程中，时间延迟是不可避免的，这影响了 CACC 车辆系统的稳定性。该文提出了一种基于 Bi-LSTM 模型的信息补偿方法。首先，建立了 CACC 车辆系统的三阶动力学，并提出了前、前、后车辆的控制策略;基于 Routh-Hurwitz 稳定性准则和频域方法推导了 CACC 车辆系统无时间延迟的局部稳定性和弦稳定性条件，揭示了模型参数与控制器参数之间的关系。对于具有时延的 CACC 车辆系统，相应地使用类似的方法获得确保局部稳定性和弦稳定性的最大时延。然而，当时间延迟超过最大值时，CACC 车辆系统的稳定性就会被破坏。为了应对时间延迟的影响，采用双向长短期记忆 （Bi-LSTM） 模型来预测和重构受时间延迟影响的信息。此外，还设置了相关参数，并使用真实车辆数据进行计算和仿真。仿真结果证实了可以保证局部和弦的稳定性，并进一步表明该文中 CACC 车辆系统的最大时延边界可能达到 0.45s。 为了突出Bi-LSTM的优越性，通过将LSTM和KF与BiLSTM进行比较，仿真结果表明Bi-LSTM具有最高的相关系数和最小的均方根误差，验证了Bi-LSTM重建受时间延迟影响的信息比KF和LSTM更有效。