On the inherent robustness of optimal and suboptimal nonlinear MPC

The authors of Yu et al. (2014) noted that the result in Pannocchia et al. (2011) applied only to systems with continuous optimal cost functions. However, discontinuous optimal cost functions may be present in systems with hard terminal region constraints. We include a simple example of a continuous dynamical system with a provably discontinuous optimal value function that, as a consequence of the main result of this work, is inherently robust. This example is to our knowledge the first such system reported in the literature.