Longitudinal control strategy for a class of vehicles following systems based on random factor with delays

Considering time delays factors and random factors, the stability and control strategy for a class of stochastic vehicle following systems with delays are studied. By applying vector Lyapunov function method, sufficient conditions for exponential stability of the system are obtained. Based on the random vehicles longitudinal dynamics model, which is established by stochastic differential equation, the controller for the system is designed by sliding mode control method. According to the obtained results, the system stability is researched. Finally, simulation experiments are given to illustrate the obtained control strategy. Simulation results showed that in less than 5s, the accelerations and the speeds of the following vehicles converge to the leading vehicle, and the vehicle spacing errors approached to less than 0.05 m.