A novel robust nonlinear model predictive control strategy is proposed for
systems with convex dynamics and convex constraints. Using a sequential convex
approximation approach, the scheme constructs tubes that contain predicted
trajectories, accounting for approximation errors and disturbances, and
guaranteeing constraint satisfaction. An optimal control problem is solved as a
sequence of convex programs, without the need of pre-computed error bounds. We
develop the scheme initially in the absence of external disturbances and show
that the proposed nominal approach is non-conservative, with the solutions of
successive convex programs converging to a locally optimal solution for the
original optimal control problem. We extend the approach to the case of
additive disturbances using a novel strategy for selecting linearization points
and seed trajectories. As a result we formulate a robust receding horizon
strategy with guarantees of recursive feasibility and stability of the
closed-loop system