A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model

Abstract

A feedback control method with consideration of the next-nearest-neighbor interactions is investigated in the lattice hydrodynamic traffic model. The stability condition is obtained by discussing the first-order transfer function G1 and the second-order transfer function G2. The solution of mKdV equation which describe the density wave are yielded by nonlinear analysis. Theoretical analysis result indicates that the feedback gain λ, the weight coefficient of the nearest-neighbor interaction and the next-nearest-neighbor interaction have a great impact on the improvement of the stability of traffic flow. Numerical simulations by analyzing the short-term, long-term behaviors and hysteresis loop of traffic flow verify that the impacts of the feedback gain λ, the nearest-neighbor weight and the next-nearest-neighbor weight on traffic control. The feedback control method considering the next-nearest-neighbor interactions displays the nonlocal characteristics in the implementation of local control process.