An Interval Arithmetic Approach to Input-Output Reachability

The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and control of systems. The computation of the set of outputs commonly referred to as the reachable set of the system is, in many cases, intensive and a simple overestimation of it is preferred, instead. There are several perspectives to address this problem including set-based approaches, Mixed-Monotonicity, Hamilton-Jacobi reachability, neural networks, and recently reachability via Chen-Fliess series. In the present work, a Chen-Fliess series representing the input-output behavior of a dynamical system along with interval arithmetic is used to overestimate the reachable set of a system. The advantage of this combination of techniques is that it provides a closed-form of the overestimating set. Examples are presented to illustrate the results.