  Robust Model Predictive Control (MPC) for nonlinear systems is a problem that
poses significant challenges as highlighted by the diversity of approaches
proposed in the last decades. Often compromises with respect to computational
load, conservatism, generality, or implementation complexity have to be made,
and finding an approach that provides the right balance is still a challenge to
the research community. This work provides a contribution by proposing a novel
shrinking-horizon robust MPC formulation for nonlinear discrete-time systems.
By explicitly accounting for how disturbances and linearization errors are
propagated through the nonlinear dynamics, a constraint tightening-based
formulation is obtained, with guarantees of robust constraint satisfaction. The
proposed controller relies on iteratively solving a Nonlinear Program (NLP) to
simultaneously optimize system operation and the required constraint
tightening. Numerical experiments show the effectiveness of the proposed
controller with three different choices of NLP solvers as well as significantly
improved computational speed, better scalability, and generally reduced
conservatism when compared to an existing technique from the literature.
