Robust Under-Approximations and Application to Reachability of Non-Linear Control Systems with Disturbances

We describe a set-based approach, relying on mean-value extensions, for computing guaranteed under-approximations of ranges (or images) of continuously differentiable functions f from mathbb {R}{m} to mathbb {R}{n} , including what we call robust ranges, i.e., ranges of functions under adversarial uncertainties. Our method is capable of computing efficiently, at a low computational cost, full n -dimensional subsets of the image of f. As an application, we show how to compute under-approximations of robust reachable sets of non-linear controlled dynamical systems under time-varying uncertainties, which is central to many verification problems in control theory.