Mean Value Form Enclosures for Nonlinear Reachability Analysis

This paper presents a new method for computing time-varying enclosures of the reachable sets of nonlinear systems subject to bounded uncertainties, which has applications in set-based state estimation, fault detection, robust control, etc. Interval reachability methods based on differential inequalities (DI) are desirable in these applications due to their high efficiency, but they often produce extremely conservative bounds. Here, we extend the DI approach to compute tighter enclosures using the so-called mean value form, which is widely used to mitigate the conservatism of interval methods in non-dynamic settings. This method is shown to be much more accurate than interval DI and more efficient than a related approach using Taylor models for a challenging case study.

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