Nonlinear cruise controllers with bidirectional sensing for a string of vehicles

Abstract

We introduce a nonlinear cruise controller that is fully decentralized (by vehicle) and uses spacing and speed measurements from the preceding and following vehicles to decide on the appropriate control action (acceleration) for each vehicle. The proposed cruise controller is studied on both a ring-road and an open road and guarantees that there are no collisions between vehicles, while their speeds are always positive and never exceed the road speed limits. For both cases of the open road and the ring-road, we rigorously prove that the set of equilibrium points is globally asymptotically stable and provide $KL$ estimates that guarantee uniform convergence to the said set. Moreover, we show that for the ring-road, and under certain conditions, there is a single equilibrium point which is exponentially attractive. Finally, for the case of an open road we provide (small-signal) $L^2$ string stability estimates and demonstrate numerically that also $L^{\infty }$ string stability holds.