  This paper presents a method for calculating Region of Attraction of a target
set (not necessarily an equilibrium) for controlled polynomial dynamical
systems, using a hierarchy of semidefinite programming problems (SDPs). Our
approach builds on previous work and addresses its main issue, the fast-growing
memory demands for solving large-scale SDPs. The main idea in this work is in
dissecting the original resource-demanding problem into multiple smaller,
interconnected, and easier to solve problems. This is achieved by
spatio-temporal splitting akin to methods based on partial differential
equations. We show that the splitting procedure retains the convergence and
outer-approximation guarantees of the previous work, while achieving higher
precision in less time and with smaller memory footprint.
