考虑下游平均优化车流量的延迟反馈控制方法

A Feedback Control Scheme with Consideration of the Downstream Average Optimal Traffic Flow

关键词:  格子流体力学模型  反馈控制  稳定性分析  非线性分析  扭结-反扭结波

Key words:  lattice hydrodynamic model  feedback control  stability analysis  nonlinear analysis  kink-anti-kink wave

摘要:

为实现对交通流拥堵的抑制,基于格子流体力学模型引入下游平均优化车流量与当前延迟车流量的差作为反馈控制。首先，通过对控制方程的稳定性分析，利用Hurwitz准则判断特征多项式ds的稳定性，得到控制方程满足交通控制理论定义的第一个条件。再根据传递函数的H_∞范数的条件，得出控制方程的稳定性条件。采用非线性分析的约化摄动方法推导出mKdV方程，得到描述交通拥堵的扭结-反扭结密度波解。结果表明，增加反馈增益λ和反应时间t_d可以提高交通控制系统的稳定性。通过数值模拟，其仿真结果与理论结果吻合较好。基于格子流体力学模型，考虑把下游平均优化车流量与当前延迟车流量之差作为一种延迟反馈控制方案，可以有效抑制交通拥堵，有利于交通系统的稳定。

Abstract:

In order to achieve the suppression of traffic congestion,the difference between the downstream average optimized traffic flow and the current delayed traffic flow is introduced as feedback control based on the lattice hydrodynamic model.Firstly,through the stability analysis of the control equation,the stability of the characteristic polynomial ds is judged by Hurwitz criterion,and the first condition that the control equation satisfies the definition of traffic control theory is obtained.According to the H_∞ norm condition of the transfer function,the stability condition of the control equation is obtained.The mKdV equation is derived by the reduced perturbation method of nonlinear analysis,and the kink-anti-kink density wave solution describing traffic congestion is obtained.The results show that increasing the feedback gain λ and the retarded reaction time t_d can improve the stability of traffic control system.Through numerical simulation,the simulation results are in good agreement with the theoretical results.Based on the lattice hydrodynamic model,the difference between the downstream average optimization rate flow and the current delayed flow is considered as a delayed feedback control scheme,which can effectively suppress traffic congestion and is conducive to the stability of the transportation system.