Optimal Control of Connected Vehicle Systems With Communication Delay and Driver Reaction Time

In this paper, linear quadratic regulation is used to obtain an optimal design of connected cruise control (CCC). We consider vehicle strings where a CCC vehicle receives position and velocity signals through wireless vehicle-to-vehicle communication from multiple vehicles ahead. Communication delay, driver reaction time, and heterogeneity of vehicles are considered. The optimal feedback law is obtained by minimizing a cost function defined by headway and velocity errors and the acceleration of the CCC vehicle on an infinite horizon. We show that, by decomposing the optimization problem, the feedback gains can be obtained recursively as signals from vehicles farther ahead become available, and that the gains decay exponentially with the number of cars between the source of the signal and the CCC vehicle. Such properties allow graceful degradation of CCC performance under imperfect communication. The effects of the cost function on the head-to-tail string stability are also investigated and the robustness against variations in human parameters is tested. The analytical results are verified by numerical simulations at the nonlinear level. The results allow us to significantly reduce the complexity of CCC design.