  In this paper, we present conditions under which the terminal ingredients,
defined by discrete-time control barrier function (DTCBF) certificates,
guarantee recursive feasibility in nonlinear MPC. Further, we introduce the
notion of quasi-DTCBF (qDTCBF) certificates. Compared to DTCBFs, qDTCBF
conditions can be satisfied with tighter control input bounds, which is highly
advantageous if only limited actuation is possible. Both certificates encourage
an earlier reaction of the control system and result in a lower cumulative MPC
cost. The methodology is applied to a lane merging problem in automated
driving, in which DTCBF and qDTCBF certificates subject to input constraints
form the terminal ingredients to guarantee recursive feasibility of the
nonlinear MPC scheme. A simulation study demonstrates the efficacy of the
concept.
