New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect

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.

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