Spatio-Temporal Decomposition of Sum-of-Squares Programs for the Region of Attraction and Reachability

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