A Nonlinear Bidirectional Cruise Controller for Lane-Based Vehicle Motion

In this paper we introduce a nonlinear bidirectional cruise controller that uses spacing and speed measurements from the preceding and following vehicles to decide on the appropriate control action (acceleration). 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. Finally, we show that the solutions of the closed-loop system are Lagrange stable and provide certain conditions under which we also have exponential convergence to the set of equilibrium points.