  This paper develops a controller for Connected and Automated Vehicles (CAVs)
traversing a single-lane roundabout. The controller simultaneously determines
the optimal sequence and associated optimal motion control jointly minimizing
travel time and energy consumption while providing speed-dependent safety
guarantees, as well as satisfying velocity and acceleration constraints. This
is achieved by integrating (a) Model Predictive Control (MPC) to enable
receding horizon optimization with (b) Control Lyapunov-Barrier Functions
(CLBFs) to guarantee convergence to a safe set in finite time, thus providing
an extended stability region compared to the use of classic Control Barrier
Functions (CBFs). The proposed MPC-CLBF framework addresses both infeasibility
and myopic control issues commonly encountered when controlling CAVs over
multiple interconnected control zones in a traffic network, which has been a
limitation of prior work on CAVs going through roundabouts, while still
providing safety guarantees. Simulations under varying traffic demands
demonstrate the controller's effectiveness and stability.
