Considering the driver’s memory effect and new feedback control signal, a novel two-dimensional lattice hydrodynamic model is proposed. The linear stability condition of the new model is derived by exploiting control method. Via nonlinear analysis, the kink–antikink solution of modified Korteweg–de Vries (mKdV) equation is derived, which can be used to give a description of the density waves near the critical points. Then numerical simulation is conducted to verify the theoretical analysis. The results of theoretical analysis and numerical simulation both show that the new control signal availably stabilizes the traffic flow. On the contrary, as the driver’s memory time increases, the traffic flow becomes more unstable.

考虑驾驶员的记忆效应和新的反馈控制信号，提出了一种新型的二维晶格流体动力学模型。利用控制方法推导了新模型的线性稳定性条件。通过非线性分析，得出了改进的Korteweg-de Vries（mKdV）方程的扭结-抗扭结解，可用于描述临界点附近的密度波。然后进行了数值模拟，以验证理论分析。理论分析和数值模拟的结果均表明，新的控制信号有效地稳定了交通流量。相反，随着驾驶员的记忆时间增加，交通流变得更加不稳定。