  The paper introduces novel families of cruise controllers for autonomous
vehicles on lane-free ring-roads. The design of the cruise controllers is based
on the appropriate selection of a Control Lyapunov Function expressed on
measures of the energy of the system with the kinetic energy expressed in ways
similar to Newtonian or relativistic mechanics. The derived feedback laws
(cruise controllers) are decentralized (per vehicle), as each vehicle
determines its control input based on: (i) its own state; (ii) either only the
distance from adjacent vehicles (inviscid cruise controllers) or the state of
adjacent vehicles (viscous cruise controllers); and (iii) its distance from the
boundaries of the ring-road. A detailed analysis of the differences and
similarities between lane-free straight roads and lane-free ring-roads is also
presented.
