Analysis of the historical time integral form of relative flux and feedback control in an extended lattice hydrodynamic model

An extended lattice hydrodynamic model is presented by considering the historical relative flux in integral form and flux change rate. The flux change rate can be regarded as the control signal. Control method is applied to the linear stability analysis and the stability condition of the model is obtained. In addition, energy consumption is also explored. To prove the theoretical findings, numerical simulations are carried out in this paper. Simulation results show that the historical relative flux can worsen the traffic flow stability and increase the energy consumption. The control signal plays a significant role in stabilizing the traffic flow and leading to a lower energy consumption. The simulation results are found consistent with the theoretical results. (C) 2019 Elsevier B.V. All rights reserved.