Robust Reachable Set

Abstract

Reachable set computation is one of the primary techniques for safety verification of linear dynamical systems. In reality the underlying dynamics have uncertainties like parameter variations or modeling uncertainties. Therefore, the reachable set computation must consider the uncertainties in the dynamics to be useful i.e . the computed reachable set should be over or under approximation if not exact. This paper presents a technique to compute reachable set of linear dynamical systems with uncertainties. First, we introduce a construct called support of a matrix. Using this construct, we present a set of sufficient conditions for which reachable set for uncertain linear system can be computed efficiently; and safety verification can be performed using bi-linear programming. Finally, given a linear dynamical system, we compute robust reachable set, which accounts for all possible uncertainties that can be handled by the sufficient conditions presented. Experimental evaluation on benchmarks reveal that our algorithm is computationally very efficient.