Forward Completeness in Open Sets and Applications to Control of Automated Vehicles

Forward complete systems are guaranteed to have solutions that exist globally for all positive time. In this article, a relaxed Lyapunov-like condition for forward completeness is presented for finite-dimensional systems defined on open sets that does not require boundedness of the Lyapunov-like function along the solutions of the system but an exponential growth condition. The corresponding condition is then exploited for the design of autonomous 2-D movement, with focus on lane-free cruise controllers for automated vehicles described by the bicycle kinematic model. The derived feedback laws (cruise controllers) are decentralized and can account for collision avoidance, roads of variable width, on-ramps and off-ramps as well as different desired speed for each vehicle.