Reachability Analysis for Linear Discrete Time Set–Dynamics Driven by Random Convex Compact Sets

This paper studies linear set–dynamics driven by random convex compact sets (RCCSs), and derives the set–dynamics of the expectations of the associated reach sets as well as the dynamics of the corresponding covariance functions. It is established that the expectations of the reach sets evolve according to deterministic linear set–dynamics while the associated dynamics of covariance functions evolves on the Banach space of continuous functions on the dual unit ball. The general framework is specialized to the case of Gaussian RCCSs, and it is shown that the Gaussian structure of random sets is preserved under linear set–dynamics of random sets.