Establishment, maintenance, and re-establishment of the safe and efficient steady-following state

We present an integrated mathematical model of vehicle-following control for the establishment, maintenance, and re-establishment of the previous or new safe and efficient steady-following state. The hyperbolic functions are introduced to establish the corresponding mathematical models, which can describe the behavioral adjustment of the following vehicle steered by a well-experienced driver under complex vehicle following situations. According to the proposed mathematical models, the control laws of the following vehicle adjusting its own behavior can be calculated for its moving in safety, efficiency, and smoothness (comfort). Simulation results show that the safe and efficient steady-following state can be well established, maintained, and re-established by its own smooth (comfortable) behavioral adjustment with the synchronous control of the following vehicle's velocity, acceleration, and the actual following distance.