Bounding the uncertainity in nonlinear robust model predictive control using sphere covering

We consider nonlinear continuous-time systems with additive model uncertainty. We design controllers based on a receding horizon optimization strategy, and we propose a new method to bound the uncertainty along the predicted trajectories. The bounds derived here are less conservative compared to existing methods, because the proposed method limits the exponential growth of the invariant cones around the nominal predicted trajectories. This is achieved by applying results from computational geometry, which allows us to cut and reset the width of the mouth of these cones through tunable control parameters. The method does not impose specific constraints on the structure of the uncertain term in the equations, other than assuming that it is locally Lipschitz and upper bounded.