  We consider the merging control problem for Connected and Automated Vehicles
(CAVs) aiming to jointly minimize travel time and energy consumption while
providing speed-dependent safety guarantees and satisfying velocity and
acceleration constraints. Applying the joint optimal control and control
barrier function (OCBF) method, a controller that optimally tracks the
unconstrained optimal control solution while guaranteeing the satisfaction of
all constraints is efficiently obtained by transforming the optimal tracking
problem into a sequence of quadratic programs (QPs). However, these QPs can
become infeasible, especially under tight control bounds, thus failing to
guarantee safety constraints. We solve this problem by deriving a
control-dependent feasibility constraint corresponding to each CBF constraint
which is added to each QP and we show that each such modified QP is guaranteed
to be feasible. Extensive simulations of the merging control problem illustrate
the effectiveness of this feasibility guaranteed controller.
