  In this paper, a proof of asymptotic stability for the combined
system-optimizer dynamics associated with a class of real-time methods for
equality constrained nonlinear model predictive control is presented. General
Q-linearly convergent online optimization methods are considered and asymptotic
stability results are derived for the case where a single iteration of the
optimizer is carried out per sampling time. In particular, it is shown that, if
the underlying sampling time is sufficiently short, asymptotic stability can be
guaranteed. The results constitute an extension to existing attractivity
results for the well-known real-time iteration strategy.
