An optimal consensus to guarantee the stability and crash avoidance of large-scale traffic flow in presence of time delay

A new safe optimal consensus procedure is presented to guarantee the asymptotic and string stability as well as crash avoidance of large-scale non-identical traffic flow. Since time delay is an inherent characteristic of physical actuators and sensors, measurement delay and lags are involved in the upper level control structure. A third-order linear model is employed to define the 1-D motion of each automated vehicle (AV) and the constant time headway plan is employed to regulate the inter-AV distance. It is assumed that the network structure is decentralized look ahead (DLA) and each AV has access to relative position and velocity regarding with the front AV. A linear control law is introduced for each AV and by performing the stability analysis in frequency domain, the necessary conditions guaranteeing string stability and crash avoidance for large-scale traffic flow are derived. Afterwards, to calculate the optimal control parameters guaranteeing the best performance, an objective function combining all mentioned conditions as well as maximum overshoot, settling time and stability margin is introduced. The genetic algorithm (GA) technique is employed to optimize the presented objective function and obtain the optimal control parameters. Various numerical results are proposed to demonstrate the efficiency of this method.