摘要：AbstractIn order to be useful in applications, model predictive control (MPC) must be robust to small disturbances. Continuity of the regulator’s optimal value function would ensure a measure of robustness, but, in general, there is no guarantee that this function is continuous. Here we present an inherent robustness result for a broad class of systems that have a (not necessarily robust) positive invariant set that is disjoint from the set of discontinuities of the optimal value function. If this set attracts every set in the domain of robustness in a single control move, the system is robustly stable. We demonstrate this result with the notorious (u, u3) example, which has an optimal value function that is discontinuous on every neighborhood of its target, and establish that MPC is still robust.
