Self-stabilizing lattice model with feedback-feedforward coupling and its nonlinear stability analysis

To mitigate traffic congestion, this paper integrates historical traffic flow difference-based feedback and density self-expectation-based feedforward to develop a feedback-feedforward coupled self-stabilizing strategy, and proposes a novel traffic flow lattice model. Using linear stability theory and nonlinear analysis, we investigate the strategy’s mechanism on macroscopic traffic flow stability, deriving the model’s linear stability criterion, and the modified Korteweg-de Vries (mKdV) equation (with its density wave solution) describing congestion propagation near the critical point. Theoretical and simulation results show that, compared with single-information self-stabilizing strategies, the proposed strategy significantly enhances traffic flow stability and robustness, and accelerates disturbance convergence to a steady state. Longer time intervals in the strategy further improve stability and congestion suppression. This research provides new theoretical insights for alleviating traffic congestion.