A reinterpretation of set differential equations as differential equations in a Banach space

Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example, which can be treated in support function representation, but not in the Hukuhara setting

Towards optimal space-time discretization for reachable sets of nonlinear control systems

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial discretizations of Euler's method for reachable set computation in a non-uniform way to improve the performance of the method