Robust receding horizon control for convex dynamics and bounded disturbances

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.